A134698 Self-power numbers (or SPN's): numbers n with property that for each single digit d of n, we can also see the decimal expansion of the d-th power of some number as a substring of n and also n contains no 0's or 1's.

32564, 232564, 256432, 322564, 325642, 325643, 325644, 325645, 325646, 325648, 325664, 332564, 432564, 532564, 632564, 643256, 832564, 2232564, 2256432, 2322564, 2325642, 2325643, 2325644, 2325645, 2325646, 2325648, 2325664, 2332564, 2432564, 2532564

Offset: 1

Author

Eric Angelini, Jul 05 2005

Keywords

• nonn
• base

Comments

Computed by M. F. Hasler, Feb 02 2008, Feb 03 2008

There are an infinite number of SPN's, since for example we can prefix n by any digit of n.

Examples

			n = 32564 is a member because we can see a cube (64) in n, a square (4 or 25), a fifth power (32), a sixth power (64) and a fourth power (256).
		

Links

• M. F. Hasler, Table of n, a(n) for n = 1..1158

Crossrefs

Cf. A134949, A134947, A134439, A134692, A134948.

Extensions

More terms from M. F. Hasler, Feb 02 2008