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

Author

Bernard Schott, Mar 28 2022

Keywords

• nonn
• base

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.

Examples

			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.
		

Links

• Diophante, A389 - Les décaXphobes (in French).

Crossrefs

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

Programs

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

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.

Extensions

More terms from Jinyuan Wang, Mar 28 2022