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

1,3

Comments

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.

Links

Table of n, a(n) for n=1..35.

Example

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.

Prog

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

Crossrefs

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

Sequence in context: A018319 A100095 A227922 * A013626 A067701 A059240

Adjacent sequences: A179779 A179780 A179781 * A179783 A179784 A179785

Keyword

base,nonn

Author

Jonathan Vos Post, Jul 27 2010

Extensions

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

Status

approved