A331604 Lexicographically earliest sequence of distinct positive terms such that a(n), a(n+1) and a(n) + a(n+1) have at least one digit in common.

1, 10, 11, 91, 12, 19, 79, 78, 8, 80, 18, 13, 23, 2, 20, 22, 102, 14, 17, 57, 58, 28, 24, 40, 4, 41, 43, 30, 3, 31, 32, 92, 29, 69, 67, 7, 70, 27, 25, 50, 5, 45, 49, 90, 9, 89, 98, 82, 42, 104, 15, 16, 46, 48, 38, 35, 103, 21, 81, 51, 54, 94, 47, 127, 61, 6, 56, 59, 39, 34, 114, 71, 76, 60, 26, 36

Offset

1,2

Links

Carole Dubois, Table of n, a(n) for n = 1..5001

Example

1, 10, 11, 91, 12, 19, 79, 78, 8,
a(1) = 1, a(2) = 10 and 11 (sum 1 + 10) have at least the digit 1 in common;
a(2) = 10, a(3) = 11 and 21 (sum 10 + 11) have at least the digit 1 in common;
a(3) = 11, a(4) = 91 and 102 (sum 11 + 91) have at least the digit 1 in common;
a(4) = 91, a(5) = 12 and 103 (sum 91 + 12) have at least the digit 1 in common;
a(5) = 12, a(6) = 19 and 31 (sum 12 + 19) have at least the digit 1 in common;
a(6) = 19, a(7) = 79 and 98 (sum 19 + 79) have at least the digit 9 in common;
a(7) = 79, a(8) = 78 and 157 (sum 79 + 78) have at least the digit 7 in common; etc.

Mathematica

Nest[Append[#1, Block[{k = 2}, While[Nand[FreeQ[#1, k], Length@ Intersection[#2, IntegerDigits[k], IntegerDigits[k + #1[[-1]] ]] > 0], k++]; k]] & @@ {#, IntegerDigits[#[[-1]] ]} &, {1}, 75] (* Michael De Vlieger, Jan 21 2020 *)

Crossrefs

Cf. A331626 (the three terms have no digit in common).

Sequence in context: A228381 A262229 A347182 * A086457 A046851 A045953

Adjacent sequences: A331601 A331602 A331603 * A331605 A331606 A331607

Keyword

base,nonn

Author

Eric Angelini and Carole Dubois, Jan 21 2020

Status

approved