A253387 A "mod sequence" where a(n) is the eventual constant value attained by the sequence defined as b(1) = n, b(m) = (Sum_{k=1..m-1} b(k)) mod m.

97, 97, 1, 1, 2, 2, 2, 2, 316, 316, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 12, 12, 4, 4, 4, 4, 12, 12, 11, 11, 11, 11, 316, 316, 11, 11, 316, 316, 316, 316, 6, 6, 316, 316, 316, 316, 316, 316, 316, 316, 97, 97, 316, 316, 316, 316, 13, 13, 316, 316, 13

Offset

1,1

Comments

The necessary and sufficient condition for the constant value a(n) to be attained by the sequence b(m) is: Sum_{k=1..m-1} b(k) = b(m)*(m + 1). - Lechoslaw Ratajczak, Sep 15 2025

Links

Lechoslaw Ratajczak, Table of n, a(n) for n = 1..1000 (terms 1..448 from Jean-François Alcover)

MathOverflow, Mod sequences that seem to become constant

Example

a(5) = 2, because the b sequence is 5, 1, 0, 2, 3, 5, 2, 2, 2, 2, 2, ...

Prog

(Maxima) (a(n):=(s:n, b:0, for m:2 unless s=b*(m+1) do (b:mod(s, m), s:s+b), b),
makelist(a(n), n, 1, 100)); /* Lechoslaw Ratajczak, Sep 15 2025 */
(PARI) a(n) = my(s=n, m=2, b=0); while(s!=b*(m+1), b=s % m; s += b; m++); b \\ Andrew Howroyd, Sep 15 2025

Crossrefs

Cf. A074482, A117846.

Sequence in context: A126146 A112667 A106419 * A074482 A130765 A111326

Adjacent sequences: A253384 A253385 A253386 * A253388 A253389 A253390

Keyword

sign

Author

Jean-François Alcover, Dec 31 2014

Status

approved