A377403 For n >= 2, a(n) is the number of iterations needed for the map: x -> x / A085392(x) if A085392(x) > 1, otherwise x -> x + A151800(x), to (the first occurrence of) 2.

0, 3, 1, 3, 1, 3, 2, 4, 1, 4, 2, 3, 1, 4, 3, 4, 2, 3, 2, 4, 1, 3, 3, 4, 1, 5, 2, 4, 2, 3, 4, 4, 1, 4, 3, 3, 1, 4, 3, 4, 2, 4, 2, 5, 1, 4, 4, 4, 2, 4, 2, 5, 3, 4, 3, 4, 1, 5, 3, 7, 1, 5, 5, 4, 2, 3, 2, 4, 2, 6, 4, 4, 1, 5, 2, 4, 2, 5, 4, 6, 1, 3, 3, 4, 1, 4, 3, 3, 3, 4, 2, 4, 1, 4, 5, 4, 2, 5, 3, 4, 2, 4, 3, 5, 1, 6, 4, 3, 2, 4, 4, 6, 2, 4, 2, 5, 1, 4, 4, 5

Offset

2,2

Comments

Also a(2*k + 1) = A001222(2*k + 1) + 2 + s, where s >= 1 for k = 5, 8, 14, 20, 21, 23, 26, 29, 30, 35, 36, 39, 48, 50, 51, ...

Links

Table of n, a(n) for n=2..121.

Formula

For n even: a(n) = A001222(n) - 1.

For n odd: a(n) = A001222(n) - 1 + A001222(A013634(A020639(n))).

Example

n = 3: 3 -> 8 -> 4 -> 2, 3 iterations needed to reach 2, thus a(3) = 3.
n = 9: 9 -> 3 -> 8 -> 4 -> 2, 4 iterations needed to reach 2, thus a(9) = 4.
n = 11: 11 -> 24 -> 8 -> 4 - > 2, 4 iterations needed to reach 2, thus a(11) = 4.

Mathematica

a[2] = 0; a[n_] := -1 + Length@ NestWhileList[If[CompositeQ[#], #/FactorInteger[#][[-1, 1]], # + NextPrime[#]] &, n, # > 2 &]; Array[a, 120, 2] (* Amiram Eldar, Oct 27 2024 *)

Crossrefs

Cf. A001222, A013634, A020639, A085392, A107286, A151800.

Sequence in context: A335182 A319992 A255894 * A135023 A367805 A087822

Adjacent sequences: A377400 A377401 A377402 * A377404 A377405 A377406

Keyword

nonn

Author

Ctibor O. Zizka, Oct 27 2024

Status

approved