A325114 Integers k such that no nonzero subsequence of the decimal representation of k is divisible by 7.

1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 16, 18, 19, 20, 22, 23, 24, 25, 26, 29, 30, 31, 32, 33, 34, 36, 38, 39, 40, 41, 43, 44, 45, 46, 48, 50, 51, 52, 53, 54, 55, 58, 59, 60, 61, 62, 64, 65, 66, 68, 69, 80, 81, 82, 83, 85, 86, 88, 89, 90, 92, 93, 94, 95, 96, 99, 100, 101, 102, 103, 104, 106, 108, 109, 110, 111, 113, 115, 116, 118, 120

Offset

1,2

Comments

Does not contain 114 (helps to distinguish this from related sequences).

From David A. Corneth, Sep 10 2024: (Start)

Any term greater than 10^6 must have a digit 0. Proof: Any term between 10^6 and 10^7 has a 0.

Proof via induction and contradiction; any 7 digital number term has a digit 0. Suppose some number with k with q > 7 digits has no digit 0. Then floor(k/10) is a term and has no digit 0 and q - 1 digits. But there is no such number. A contradiction. Therefore any term with at least 7 digits has a digit 0. (End)

Links

David A. Corneth, Table of n, a(n) for n = 1..10000

David A. Corneth, PARI program

Mathematica

With[{k = 7}, Select[Range@ 100, NoneTrue[DeleteCases[FromDigits /@ Rest@ Subsequences[IntegerDigits@ #], 0], Mod[#, k] == 0 &] &]] (* Michael De Vlieger, Mar 31 2019 *)

Prog

(PARI) \\ See Corneth link

Crossrefs

Cf. A014261 (for 2), A325112 (for 3), A325113 (for 4), A261189 (for 5).

See A376046 for complement.

Sequence in context: A356939 A113619 A376047 * A396939 A004765 A247063

Adjacent sequences: A325111 A325112 A325113 * A325115 A325116 A325117

Keyword

nonn,base

Author

Jonathan Kal-El Peréz, Mar 27 2019

Extensions

More than the usual number of terms are shown in order to distinguish this from a new sequence arising from the game of "buzz" (cf. A092433). - N. J. A. Sloane, Sep 09 2024

Status

approved