A119238 -id:A119238 - cp's OEIS frontend

A179782 Numbers n such that the decimal representation of n is contained as substring in that of the n-th pentagonal number.

0, 1, 5, 7, 25, 67, 482, 551, 625, 667, 2937, 6667, 9284, 9376, 9649, 48179, 49900, 55712, 66667, 89517, 90625, 161579, 631206, 666667, 890625, 1348613, 2089517, 3863187, 4999000, 6666667, 7109376, 7477735, 8575619, 10721030, 12890625

Offset: 1

Jonathan Vos Post, Jul 27 2010

This is to pentagonal numbers A000326 as A119238 is to triangular numbers A000217 and as A018834 is to squares A000290. All numbers of the form (10^n-1)/3*2+1 are contained in this list {1, 7, 67, 667, 6667, 66667, 666667, 6666667, 66666667, ...} Alois P. Heinz. Extension: Values 8-25 by Claudio Meller, 26-37 by D. S. McNeil.

			The 5th pentagonal number, 35, which contains 5.
The 7th pentagonal number, 70, which contains 7.
The 25th pentagonal number, 925, which contains 25.
The 67th pentagonal number, 6700, which contains 67.
The 482nd pentagonal number, 348245, which contains 482.
The 667th pentagonal number, 667000, which contains 667.

Cf. A000217, A000290, A000326, A018834, A067275, A119238.

[n for n in range(10**4) if str(n) in str((3*n**2-n)//2)]

Code clarified by D. S. McNeil, Aug 08 2010

cp's OEIS Frontend

A179782 Numbers n such that the decimal representation of n is contained as substring in that of the n-th pentagonal number.

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