A352317 Numbers m such that A352688(m) = 1.

3, 9, 10, 12, 18, 19, 21, 27, 28, 30, 36, 37, 39, 45, 46, 48, 54, 55, 57, 63, 64, 66, 72, 73, 75, 81, 82, 84, 90, 91, 93, 99, 100, 102, 108, 109, 111, 117, 118, 120, 126, 127, 129, 135, 136, 138, 144, 145, 147, 153, 154, 156, 162, 163, 165, 171, 172, 174, 180, 181, 183, 189, 190, 192, 198, 199

Offset

1,1

Comments

Equivalently: numbers m such that the sum of digits (A007953) of the integers from 1 to A331786(m) is not divisible by m.

Numbers m such that the first run of A331786(m) consecutive numbers whose sum of digits (A007953) is not divisible by m begins at 1.

A331786(m) is the largest possible number of consecutive integers whose sum of digits is not divisible by m.

For this sequence here, A352689(m) = A331786(m).

Links

Table of n, a(n) for n=1..66.

Diophante, A389 - Les décaXphobes (in French).

Example

For m = 10, the sum of digits of the integers from 1 up to A331786(10) = 18 is not divisible by 10; then for 19, sod(19) = 10 is divisible by 10, hence 10 is a term.

Prog

(PARI) a88(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); \\ A352688
isok(m) = a88(m) == 1; \\ Michel Marcus, Apr 15 2022

Crossrefs

Cf. A007953, A331786, A352688, A352689.

A008591 \ {0} and A017173 \ {1} are subsequences.

Sequence in context: A115403 A282409 A059012 * A055063 A030354 A108865

Adjacent sequences: A352314 A352315 A352316 * A352318 A352319 A352320

Keyword

nonn,base

Author

Bernard Schott, Apr 14 2022

Extensions

More terms from Michel Marcus, Apr 15 2022

Status

approved