Self numbers: Difference between revisions

Line 1,230:

Certainly puts my previous rubbish attempts ([[Self_numbers\Phix|archived here]]) to shame.

The precise nature of the difference-pattern eludes me, I will admit.

<lang Phix>--

--

-- Base-10 self numbers by index (single or range).

-- Follows an observed sequence pattern whereby, after the initial single-digit odd numbers, self numbers are

-- grouped in runs whose members occur at numeric intervals of 11. Runs after the first one come in blocks of

-- ten: eight runs of ten numbers followed by two shorter runs. The numeric interval between runs is usually 2,

-- but that between shorter runs, and their length, depend on the highest-order digit change occurring in them.

-- This connection with significant digit change means every ten blocks form a higher-order block, every ten

-- of ~~these~~ a higher-order~~-still~~ block, ~~and so~~ ~~on.~~

-- This connection with significant digit change means every ten blocks form a higher-order block, every ten

-- of these a higher-order-still block, and so on.

--

-- The code below appears to be good up to the last self number before 10^12 — ie. 999,999,999,997, which is

-- returned as the 97,777,777,792nd such number. After this, instead of zero-length shorter runs, the actual

-- pattern apparently starts again with a single run of 10, like the one at the beginning.

--

--

integer startIndex, endIndex, counter

integer startIndex, endIndex, counter

atom currentSelf

atom currentSelf

sequence output

sequence output

function doneAfterAdding(integer interval, n)

function doneAfterAdding(integer interval, n)

-- Advance to the next self number in the sequence, append it to the output if required, indicate if finished.

-- Advance to the next self number in the sequence, append it to the output if required, indicate if finished.

for i=1 to n do

for i=1 to n do

currentSelf += interval

currentSelf += interval

counter += 1

counter += 1

if counter >= startIndex then

if counter >= startIndex then

output &= currentSelf

output &= currentSelf

end if

end if

if counter = endIndex then return true end if

if counter = endIndex then return true end if

end for

end for

return false

return false

end function

end function

function selfNumbers(sequence indexRange)

function selfNumbers(sequence indexRange)

startIndex = indexRange[1]

startIndex = indexRange[1]

endIndex = indexRange[$]

endIndex = indexRange[$]

counter = 0

counter = 0

currentSelf = -1

currentSelf = -1

output = {}

output = {}

-- Main process. Start with the single-digit odd numbers and first run.

-- Main process. Start with the single-digit odd numbers and first run.

if doneAfterAdding(2,5) then return output end if

if doneAfterAdding(2,5) then return output end if

if doneAfterAdding(11,9) then return output end if

if doneAfterAdding(11,9) then return output end if

-- If necessary, fast forward to last self number before the lowest-order block containing first number rqd.

-- If necessary, fast forward to last self number before the lowest-order block containing first number rqd.

if counter<startIndex then

if counter<startIndex then

-- The highest-order blocks whose ends this handles correctly contain 9,777,777,778 self numbers.

-- The highest-order blocks whose ends this handles correctly contain 9,777,777,778 self numbers.

-- The difference between equivalently positioned numbers in these blocks is 100,000,000,001.

-- The ~~figures~~ ~~for~~ ~~successively~~ ~~lower-order~~ ~~blocks~~ ~~have~~ ~~successively~~ ~~fewer 7s~~ ~~and~~ ~~0s!~~

-- The difference between equivalently positioned numbers in these blocks is 100,000,000,001.

-- The figures for successively lower-order blocks have successively fewer 7s and 0s!

atom indexDiff = 9777777778,

atom indexDiff = 9777777778,

numericDiff = 100000000001

numericDiff = 100000000001

while indexDiff>=98 and counter!=startIndex do

while indexDiff>=98 and counter!=startIndex do

if counter+indexDiff < startIndex then

if counter+indexDiff < startIndex then

counter += indexDiff

counter += indexDiff

currentSelf += numericDiff

currentSelf += numericDiff

else

~~indexDiff~~ = ~~(indexDiff+2)~~/~~10 -- (..78->80-~~>8)

else

indexDiff = (indexDiff+2)/10 -- (..78->80->8)

numericDiff = (numericDiff+9)/10 -- (..01->10->1)

numericDiff = (numericDiff+9)/10 -- (..01->10->1)

end if

end if

end while

end while

end if

end if

-- Sequencing loop, per lowest-order block.

-- Sequencing loop, per lowest-order block.

while true do

while true do

-- Eight ten-number runs, each at a numeric interval of 2 from the end of the previous one.

-- Eight ten-number runs, each at a numeric interval of 2 from the end of the previous one.

for i=1 to 8 do

for i=1 to 8 do

if doneAfterAdding(2,1) then return output end if

if doneAfterAdding(2,1) then return output end if

if doneAfterAdding(11,9) then return output end if

if doneAfterAdding(11,9) then return output end if

end for

end for

-- Two shorter runs, the second at an interval inversely related to their length.

-- Two shorter runs, the second at an interval inversely related to their length.

integer shorterRunLength = 8,

integer shorterRunLength = 8,

temp = floor(currentSelf/1000)

temp = floor(currentSelf/1000)

-- Work out a shorter run length based on the most significant digit change about to happen.

-- Work out a shorter run length based on the most significant digit change about to happen.

while remainder(temp,10)=9 do

while remainder(temp,10)=9 do

shorterRunLength -= 1

shorterRunLength -= 1

temp = floor(temp/10)

temp = floor(temp/10)

end while

end while

integer interval = 2

integer interval = 2

for i=1 to 2 do

for i=1 to 2 do

if doneAfterAdding(interval,1) then return output end if

if doneAfterAdding(interval,1) then return output end if

if doneAfterAdding(11,shorterRunLength) then return output end if

if doneAfterAdding(11,shorterRunLength) then return output end if

interval += (9-shorterRunLength)*13

interval += (9-shorterRunLength)*13

end for

end for

end while

end while

end function

end function

atom t0 = time()

atom t0 = time()

printf(1,"The first 50 self numbers are:\n")

printf(1,"The first 50 self numbers are:\n")

pp(selfNumbers({1, 50}),{pp_IntFmt,"%3d",pp_IntCh,false})

pp(selfNumbers({1, 50}),{pp_IntFmt,"%3d",pp_IntCh,false})

for p=8 to 9 do

for p=8 to 9 do

integer n = power(10,p)

integer n = power(10,p)

printf(1,"The %,dth safe number is %,d\n",{n,selfNumbers({n})[1]})

printf(1,"The %,dth safe number is %,d\n",{n,selfNumbers({n})[1]})

end for

end for

printf(1,"completed in %s\n",elapsed(time()-t0))</lang>

printf(1,"completed in %s\n",elapsed(time()-t0))

<pre>