A352689 -id:A352689 - cp's OEIS frontend

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

Bernard Schott, Mar 28 2022

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

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

			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.

Diophante, A389 - Les décaXphobes (in French).

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

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

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.

More terms from Jinyuan Wang, Mar 28 2022

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

Original entry on oeis.org

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

Bernard Schott, Apr 14 2022

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).

			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.

Diophante, A389 - Les décaXphobes (in French).

Cf. A007953, A331786, A352688, A352689.

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

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

More terms from Michel Marcus, Apr 15 2022

cp's OEIS Frontend

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.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

Formula

Extensions