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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 5 13:58 EST 2022. Contains 358588 sequences. (Running on oeis4.)