A326106 Lexicographically earliest sequence of distinct terms such that a(n) is not divisible by any digit of a(n+1).

1, 2, 3, 4, 5, 6, 7, 8, 9, 20, 30, 40, 33, 22, 34, 35, 23, 24, 50, 36, 55, 26, 37, 25, 27, 28, 38, 39, 29, 32, 53, 42, 44, 56, 59, 43, 45, 46, 47, 48, 57, 49, 52, 58, 54, 70, 60, 77, 62, 63, 64, 65, 66, 74, 67, 68, 69, 72, 75, 76, 73, 78, 79, 80, 90, 84, 85, 82, 83, 86, 87, 88, 93, 89, 92, 95, 94, 96, 97, 98, 99, 200, 300, 700, 303

Offset

1,2

Comments

The sequence ends with the LCM of {1, 2, 3, 4, 5, 6, 7, 8, 9} which is 2520 and we have a(1422) = 2520.

Links

Carole Dubois, Table of n, a(n) for n = 1..1422

Example

The sequence starts with 1, 2, 3, 4, 5, 6, 7, 8, 9, 20, 30, 40, 33,... and we see indeed that a(10) cannot be 10 as the digit 1 of 10 would divide 9; in the same manner, a(10) = 11 is forbidden, as are 12, 13, 14, 15, 16, 17, 18, and 19; thus a(10) = 20; etc.

Mathematica

Nest[Append[#, Block[{k = 2, n = #[[-1]]}, While[Nand[FreeQ[#, k], NoneTrue[DeleteCases[IntegerDigits@ k, 0], Mod[n, #] == 0 &]], k++]; k]] &, {1}, 84] (* Michael De Vlieger, Jun 06 2019 *)

Crossrefs

Cf. A326107, A326108, A326109, A326110 for related sequences where a(n) is divisible by exactly 1 (resp. 2, 3, 4) digit of a(n+1).

Sequence in context: A122619 A098779 A276822 * A180412 A290951 A114800

Adjacent sequences: A326103 A326104 A326105 * A326107 A326108 A326109

Keyword

base,nonn,fini

Author

Eric Angelini and Carole Dubois, Jun 06 2019

Status

approved