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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.
0
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
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
KEYWORD
base,nonn
AUTHOR
STATUS
approved