A352688 a(n) is the least term of the first run of A331786(n) consecutive numbers whose sum of digits (A007953) is not divisible by n.

9, 1, 997, 6, 7, 994, 9999993, 1, 1, 999981, 1, 9999999961, 951, 961, 9999931, 999999999999921, 1, 1, 99999999801, 1, 99999999999999601, 99501, 99601, 99999999301, 99999999999999999999201, 1, 1, 9999999999998001, 1, 999999999999999999996001, 9995001, 9996001

Offset

2,1

Comments

A331786(n) is the number of consecutive integers in the largest such possible run.

Numbers k for which a(k) = 1 are in A352317.

Links

Table of n, a(n) for n=2..33.

Diophante, A389 - Les décaXphobes (in French).

Formula

a(n) = A352689(n) - A331786(n) + 1 for n >= 2.

a(n) = 1 if n = 9*s, s > 0 (A008591), but the converse is not true.

Example

a(4) = 997 because the A331786(4) = 6 consecutive numbers 997, 998, 999, 1000, 1001, 1002 have respectively sum of digits = 25, 26, 27, 1, 2, 3 and none is divisible by 4, and there is no smaller m < 997 such that sum of digits of m, m+1, m+2, m+3, m+4, m+5 is not divisible by 4.

Prog

(PARI) a(n) = my(t=gcd(n%9, 9)); if(t<9, 10^lift(Mod(-1, n/t)/(9/t)) - 10^(n\9)*(n%9-t+1) + 1, 1); \\ Jinyuan Wang, Mar 28 2022

Crossrefs

Cf. A007953, A008591, A331786, A331788, A352317, A352689.

Sequence in context: A258437 A046761 A373776 * A335539 A193373 A246564

Adjacent sequences: A352685 A352686 A352687 * A352689 A352690 A352691

Keyword

nonn,base

Author

Bernard Schott, Mar 28 2022

Extensions

More terms from Jinyuan Wang, Mar 28 2022

Status

approved