A394761 a(n) = the length of the n-th run of 1's in A392200.

3, 3, 3, 1, 1, 3, 3, 2, 2, 1, 2, 2, 1, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 2, 2, 1, 3, 2, 2, 1, 1, 1, 2, 2, 1, 3, 2, 2, 1, 1, 1, 2, 1, 2, 3, 2, 2, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 2, 2, 1, 3, 2, 1, 2, 3, 2, 2, 1, 3, 2, 1, 2, 1, 1, 2, 2, 1, 3, 2, 2, 1, 1, 1

Offset

0,1

Comments

Alternatively, a(0) is the number of addition steps after the initial term of A381466, and a(n) is the number of addition steps after the n-th division step in A381466 for n>0.

This sequence consists of only 1s, 2s, and 3s, and at least two of those numbers appear infinitely often. In other words, a(n) is not eventually a constant sequence.

a(n) = 2 for infinitely many n if and only if gcd(A381466(2n), 2n+1) > 1 for infinitely many n, i.e. there are infinitely many odd division steps in A381466.

We conjecture that no more than eight 1's, four 2's, and three 3's can appear in a row.

Links

Sam Chapman, Table of n, a(n) for n = 0..9999

Formula

a(n) = A391446(n) - A391446(n-1) - 1 (A391446(0) is taken to be 0).

Mathematica

s={4}; a392200={}; Do[G=GCD[s[[-1]], m]; AppendTo[s, If[G==1, s[[-1]]+m, m/G]]; AppendTo[a392200, G], {m, 300}] (* increase m range for n>108 *); c=0; i=1; a394761={}; Do[While[a392200[[i]]==1, c++; i++]; AppendTo[a394761, c]; c=0; i++, {n, 87}]; a394761 (* James C. McMahon, Apr 11 2026 *)

Crossrefs

Cf. A381466, A392200, A391446.

Sequence in context: A064353 A190906 A355586 * A080311 A135368 A172358

Adjacent sequences: A394758 A394759 A394760 * A394762 A394763 A394764

Keyword

nonn

Author

Sam Chapman, Mar 31 2026

Status

approved