A392094 a(n) is the number of iterations of process A392093 applied to n required until the remaining single number equals 1.

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

Offset

1,3

Comments

Because, in process A392093, the differences are re-sorted at each iteration and used exactly once, the remaining number strictly decreases while staying positive. Hence this process terminates at 1, and a(n) is well defined.

Links

Felix Huber, Table of n, a(n) for n = 1..10000

Formula

Trivial upper bound: a(n) < n.

a(2^k) = 1 for positive integers k.

Example

a(30) = 4 since four iterations of process A392093 are required until the remaining single number equals 1: A392093(A392093(A392093(A392093(30)))) = A392093(A392093(A392093(7))) = A392093(A392093(6)) = A392093(2) = 1.

Maple

A392094 := proc(n) local a, k; k := n; a := 0; while 1 < k do k := A392093(k); a := a + 1; end do; return a; end proc: seq(A392094(n), n = 1 .. 88);

Mathematica

A392093[n_] := First[NestWhile[Union[Differences[#]] &, Divisors[n], Length[#] > 1 &]];
A392094[n_] := Length[NestWhileList[A392093, n, # > 1 &]] - 1;
Array[A392094, 100] (* Paolo Xausa, Jan 20 2026 *)

Crossrefs

Cf. A000005, A027750, A032741, A187202, A258409, A392079, A392080, A392093.

Sequence in context: A178677 A366888 A243924 * A335474 A333939 A272759

Adjacent sequences: A392091 A392092 A392093 * A392095 A392096 A392097

Keyword

nonn,easy

Author

Felix Huber, Jan 16 2026

Status

approved