A333722 -id:A333722 - cp's OEIS frontend

A333723 Successive products a(n) * a(n+1) of A333722. Each product contains a substring present both in A333722(n) and A333722(n+1).

10, 110, 132, 24, 42, 315, 75, 125, 725, 812, 672, 528, 572, 156, 96, 576, 1332, 1443, 1326, 476, 182, 39, 93, 713, 621, 1917, 497, 679, 6693, 3864, 2520, 1575, 1330, 684, 864, 384, 648, 1377, 799, 1974, 1848, 1804, 164, 184, 1840, 800, 600, 1500, 2550, 2652, 2756, 2915, 3135, 3705, 3510, 2646, 931, 1159, 3660

Offset: 1

Eric Angelini and Jean-Marc Falcoz, Apr 03 2020

			a(10) = 812 and 812 is the product of two terms containing the substring 2, which are A333722(10) = 29 and A333722(11) = 28.

Jean-Marc Falcoz, Table of n, a(n) for n = 1..2001

Cf. A333722.

A333724 Largest digit that is shared in A333722 by the pair a(n), a(n+1) and the product a(n) * a(n+1).

Original entry on oeis.org

1, 1, 1, 2, 2, 1, 5, 5, 2, 2, 2, 2, 2, 6, 6, 6, 3, 3, 3, 4, 1, 3, 3, 3, 2, 7, 7, 7, 9, 6, 5, 5, 3, 8, 8, 8, 8, 1, 7, 4, 4, 4, 4, 4, 4, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5, 4, 9, 1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 5, 5, 5, 8, 3, 3, 3, 3, 2, 2, 9, 8, 0, 0, 9, 9, 9, 9, 9, 5, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 6, 8, 7, 7, 7, 7, 7, 8

Offset: 1

Eric Angelini and Jean-Marc Falcoz, Apr 03 2020

			a(10) = 2, as 2 is the largest digit shared by A333722(10) = 29, A333722(11) = 28 and by the product 29 * 28 = 812 = A333724(10).

Jean-Marc Falcoz, Table of n, a(n) for n = 1..2210

Cf. A333722, A333723 (the products).

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.

Original entry on oeis.org

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

Jean-Marc Falcoz and Eric Angelini, Apr 10 2020

			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.

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

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 *)

cp's OEIS Frontend

A333723 Successive products a(n) * a(n+1) of A333722. Each product contains a substring present both in A333722(n) and A333722(n+1).

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A333724 Largest digit that is shared in A333722 by the pair a(n), a(n+1) and the product a(n) * a(n+1).

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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.

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Mathematica