A103662 Smallest power with base>1 and exponent n whose decimal representation doesn't contain the digit 0.

1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 9765625, 177147, 531441, 8192, 16384, 32768, 65536, 17179869184, 262144, 524288, 3833759992447475122176, 1582794342217312156827221746448942623537121214738891981, 341427877364219557396646723584, 94143178827, 16777216

Offset: 0

Author

Hugo Pfoertner, Feb 28 2005

Keywords

• nonn
• base

Comments

For statistical reasons it is conjectured that the sequence is finite.

a(40), if it exists, is not known.

From M. F. Hasler, Mar 08 2014 (Start):

Finite means here that for some n, no such power > 1 exists. This might be the case already for n=40. Alternatively, the sequence might be defined for all n by letting a(n)=1 if no larger power exists. Then a(n)=n^A103663(n) for all n.

Differs from A238938 from n=10 on. See the OEIS wiki page for further information. (End)

Examples

			base / exponent n / base^exponent
2 1 2
2 2 4
2 3 8
2 4 16
2 5 32
2 6 64
2 7 128
2 8 256
2 9 512
5 10 9765625
3 11 177147
3 12 531441
2 13 8192
2 14 16384
2 15 32768
2 16 65536
4 17 17179869184
2 18 262144
2 19 524288
12 20 3833759992447475122176
381 21 1582794342217312156827221746448942623537121214738891981
22 22 341427877364219557396646723584
3 23 94143178827
...
a(10)=9765625 because 5^10 is the smallest 10th power containing no zero in its decimal representation (2^10=1024, 3^10=59049, 4^10=1048576).
		

Links

• Michel Marcus, Table of n, a(n) for n = 0..39
• M. F. Hasler, Zeroless powers, OEIS wiki, Mar 07 2014

Crossrefs

Cf. A103663 = smallest bases x such that x^n has a zero-less decimal representation.

Programs

PARI

A103662(n)=for(b=2,9e9,vecmin(digits(b^n))&&return(b^n)) \\ M. F. Hasler, Mar 08 2014

Formula

a(n) = A103663(n)^n. - M. F. Hasler, Mar 08 2014

Extensions

a(21)=381^21 found by Joshua Zucker.

Edited by Charles R Greathouse IV, Aug 03 2010

Keyword:fini removed by Jianing Song, Jan 28 2023 as finiteness is only conjectured.