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

Author

Jean-Marc Falcoz and Eric Angelini, Apr 10 2020

Keywords

• base
• nonn

Examples

			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.
		

Crossrefs

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

Programs

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 *)