Sisyphus sequence: Difference between revisions

</pre>

=={{header|Julia}}==

<syntaxhighlight lang="julia">using Counters, Formatting, Primes

struct Sisyphus end

function Base.iterate(s::Sisyphus, state = (0, 0))

n, p = state

if n == 0

return (1, 0), (1, 0)

else

if isodd(n)

p = nextprime(p + 1)

n += p

else

n ÷= 2

end

return (n, p), (n, p)

end

end

function test_sisyphus()

coun = Counter{Int}()

println("The first 100 members of the Sisyphus sequence are:")

for (i, (n, p)) in enumerate(Sisyphus())

if n < 250

coun[n] += 1

end

if i < 101

print(rpad(n, 4), i % 10 == 0 ? "\n" : "")

elseif i in [1000, 10000, 100_000, 1_000_000, 10_000_000, 100_000_000]

print(

rpad("\n$(format(i, commas = true))th number:", 22),

rpad(format(n, commas = true), 14),

"Highest prime needed: ",

format(p, commas = true),

)

end

if i == 100_000_000

println(

"\n\nThese numbers under 250 do not occur in the first 100,000,000 terms:",

)

println(" ", filter(j -> !haskey(coun, j), 1:249), "\n")

sorteds = sort!([(p, coun[p]) for p in coun], by = last)

maxtimes = sorteds[end][2]

println(

"These numbers under 250 occur the most ($maxtimes times) in the first 100,000,000 terms:",

)

println(" ", map(first, filter(p -> p[2] == maxtimes, sorteds)))

elseif n == 36

println("\nLocating the first entry in the sequence with value 36:")

println(

" The sequence position: ",

format(i, commas = true),

" has value $n using prime ",

format(p, commas = true),

)

break

end

end

end

test_sisyphus()

</syntaxhighlight>{{out}}

<pre>

The first 100 members of the Sisyphus sequence are:

1 3 6 3 8 4 2 1 8 4

2 1 12 6 3 16 8 4 2 1

18 9 28 14 7 30 15 44 22 11

42 21 58 29 70 35 78 39 86 43

96 48 24 12 6 3 62 31 92 46

23 90 45 116 58 29 102 51 130 65

148 74 37 126 63 160 80 40 20 10

5 106 53 156 78 39 146 73 182 91

204 102 51 178 89 220 110 55 192 96

48 24 12 6 3 142 71 220 110 55

1,000th number: 990 Highest prime needed: 2,273

10,000th number: 24,975 Highest prime needed: 30,713

100,000th number: 265,781 Highest prime needed: 392,111

1,000,000th number: 8,820,834 Highest prime needed: 4,761,697

10,000,000th number: 41,369,713 Highest prime needed: 55,900,829

100,000,000th number: 1,179,614,168 Highest prime needed: 640,692,323

These numbers under 250 do not occur in the first 100,000,000 terms:

[36, 72, 97, 107, 115, 127, 144, 167, 194, 211, 214, 230, 232]

These numbers under 250 occur the most (7 times) in the first 100,000,000 terms:

[28, 7, 14]

Locating the first entry in the sequence with value 36:

The sequence position: 77,534,485,877 has value 36 using prime 677,121,348,413