Self numbers: Difference between revisions

Content added Content deleted
(→‎sliding sieve: + tidy generator)
m (→‎{{header|AppleScript}}: Simpler block interval calculation. Revamped comments.)
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<lang applescript>(*
<lang applescript>(*
Base-10 self numbers by index (single or range).
Base-10 self numbers by index (single or range).
After the initial single-digit numbers, the sequence follows an observed pattern whereby self numbers occur in groups,
After the initial single-digit numbers, the sequence follows an observed pattern whereby self numbers
the interval between consecutive numbers in a group being 11 and that between groups 2.
occur in groups whose consecutive members are 11 apart. The interval between these groups is 2.
Groups occur in blocks of ten: eight ten-number groups sandwiched between two shorter groups.
They occur in blocks of ten: eight ten-number groups sandwiched between two shorter groups.
The intervals between blocks and the lengths of the shorter groups
The intervals between blocks and the lengths of the shorter groups depend the most signficant
depend the most signficant digit to have changed at the time they're set.
digit to have changed in the number sequence since they were last set.
*)
*)
on selfNumbers(indexRange)
on selfNumbers(indexRange)
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-- Main loop.
-- Main loop.
set sentinel to thisSelf
set shortGroupLength to 10
set shortGroupLength to 10
repeat -- Per block.
repeat -- Per block.
-- First short group.
-- First short group. Its length in the first block is 10, thereafter the same as that of the second
-- Its length is initially 10, then the same as that of the second short group of the preceding block.
-- short group of the preceding block. The numeric interval preceding it is related to this length.
-- The interval before it depends on the most significant digit to have
set thisSelf to thisSelf + 2 + (10 - shortGroupLength) * 13
-- ticked over since the first (sentinel) number of the preding block.
set interval to 2
set temp1 to sentinel div 1000
set temp2 to thisSelf div 1000
repeat until (temp1 = temp2)
set interval to interval + 13
set temp1 to temp1 div 10
set temp2 to temp2 div 10
⚫
end repeat
set thisSelf to thisSelf + interval
set sentinel to thisSelf
if (storer's doneAfter(thisSelf)) then return storer's output
if (storer's doneAfter(thisSelf)) then return storer's output
-- Groups' internal intervals are all 11.
-- Consecutive numbers within groups are 11 apart.
repeat (shortGroupLength - 1) times
repeat (shortGroupLength - 1) times
set thisSelf to thisSelf + 11
set thisSelf to thisSelf + 11
if (storer's doneAfter(thisSelf)) then return storer's output
if (storer's doneAfter(thisSelf)) then return storer's output
end repeat
end repeat
⚫
-- Eight ten-number groups, each preceded by an interval of 2.
-- Eight ten-number groups, each preceded by an interval of 2.
repeat 8 times
repeat 8 times
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end repeat
end repeat
end repeat
end repeat
-- Second short group.
-- Its length depends on the most significant digit to tick over at the thousands boundary within it.
-- Second short group. Its length depends on the most significant digit to tick over
-- The interval before it is 2.
-- at the thousands boundary within it. The interval preceding it is 2.
set thisSelf to thisSelf + 2
set thisSelf to thisSelf + 2
if (storer's doneAfter(thisSelf)) then return storer's output
if (storer's doneAfter(thisSelf)) then return storer's output
Retrieved from "https://rosettacode.org/wiki/Self_numbers"