A293689 Position of the prime ant after n steps. If the value of the ant's position is prime, it steps to the right; if the value is composite, it divides by the least divisor, steps to the left, and adds the divisor.

0, 1, 2, 1, 2, 3, 4, 3, 4, 5, 6, 5, 4, 3, 2, 3, 4, 5, 6, 5, 6, 7, 6, 7, 8, 7, 8, 9, 10, 9, 10, 9, 8, 7, 8, 7, 6, 5, 6, 5, 4, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 11, 10, 9, 10, 11, 12, 13, 12, 11, 12, 13, 14, 13, 14, 13, 12, 11, 10, 9, 8, 9, 10, 11, 12, 11, 12, 13

Offset

0,3

Comments

a(n) gives the position after the n-th step on the infinite sequence (2, 3, 4, ...). If the value at the ant's position is prime, the ant steps to the right. If the value is composite, the ant divides the number by its least prime divisor, steps to the left, and adds the divisor to the new position.

Links

Peter Kagey, Table of n, a(n) for n = 0..10000

Code Golf Stack Exchange user Super Chafouin, The Prime Ant.

Example

a(0) = 0:
2 3 4 5 6 7 ...
^ (prime; step to the right)
a(1) = 1:
2 3 4 5 6 7 ...
  ^ (prime; step to the right)
a(2) = 2:
2 3 4 5 6 7 ...
    ^ (composite; divide by 2, step to the left, add 2)
a(3) = 1:
2 5 2 5 6 7 ...
  ^ (prime; step to the right)
a(4) = 2:
2 5 2 5 6 7 ...
    ^

Mathematica

NestWhileList[If[PrimeQ[#2[[#1]] ], {#1 + 1, #2}, {#1 - 1, ReplacePart[#2, {#1 - 1 -> #2[[#1 - 1]] + #3, #1 -> #2[[#1]]/#3}]} & @@ {#1, #2, FactorInteger[#2[[#1]] ][[1, 1]]}] & @@ # &, {2, Range[10^2]}, First@ # < Length@ Last@ # &, 1, 78][[All, 1]] - 2 (* Michael De Vlieger, Oct 15 2017 *)

Crossrefs

Sequence in context: A330636 A030330 A286579 * A059261 A285869 A162330

Adjacent sequences: A293686 A293687 A293688 * A293690 A293691 A293692

Keyword

nonn,walk,look

Author

Peter Kagey, Oct 14 2017

Status

approved