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A326106
Lexicographically earliest sequence of distinct terms such that a(n) is not divisible by any digit of a(n+1).
6
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
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
KEYWORD
base,nonn,fini
AUTHOR
Eric Angelini and Carole Dubois, Jun 06 2019
STATUS
approved