A333933 Lexicographically earliest sequence of distinct positive integers such that a(n), a(n+1) and the product a(n)*a(n+1) have in common the substring n.

1, 12, 23, 134, 145, 65, 567, 278, 289, 910, 110, 10112, 1213, 1413, 15014, 16154, 16817, 17018, 18719, 19201, 2120, 2218, 10223, 2324, 24251, 2526, 27026, 52827, 28291, 29303, 30310, 3231, 32733, 6334, 34351, 35036, 36373, 37388, 39385, 139240, 4041, 41428, 34342, 15443, 4445, 45461, 46847, 34847, 48149

Offset

1,2

Links

Table of n, a(n) for n=1..49.

Example

a(1) = 1, a(2) = 12 and the product a(1)*a(2) = 12 have n = 1 in common;
a(2) = 12, a(3) = 23 and the product a(2)*a(3) = 276 have n = 2 in common;
a(3) = 23, a(4) = 134 and the product a(3)*a(4) = 3082 have n = 3 in common;
a(4) = 134, a(5) = 145 and the product a(4)*a(5) = 19430 have n = 4 in common;
...
a(120) = 11912061, a(121) = 1012120 and their product 12056435179320 share the substring 120; etc.

Mathematica

a[1]=1; a[n_]:=a[n]=Block[{k=1}, While[MemberQ[Array[a, n-1], k]||!(Q=StringContainsQ)[(T=ToString)@k, T@n]||!And@@(Q[T@#, T[n-1]]&/@{a[n-1], k, a[n-1]*k}), k++]; k]; Array[a, 26] (* Giorgos Kalogeropoulos, May 12 2022 *)

Crossrefs

A333722 (presents the same idea, but without the constraint of the substring being n).

Sequence in context: A083683 A294139 A255766 * A015447 A072822 A239656

Adjacent sequences: A333930 A333931 A333932 * A333934 A333935 A333936

Keyword

base,nonn

Author

Jean-Marc Falcoz and Eric Angelini, Apr 10 2020

Status

approved