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A103662 Smallest power with base>1 and exponent n whose decimal representation doesn't contain the digit 0. 11
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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)

LINKS

Michel Marcus, Table of n, a(n) for n = 0..39

M. F. Hasler, Zeroless powers, OEIS wiki, Mar 07 2014

FORMULA

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

EXAMPLE

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).

PROG

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

CROSSREFS

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

Sequence in context: A275076 A275064 A238938 * A180211 A275075 A275063

Adjacent sequences:  A103659 A103660 A103661 * A103663 A103664 A103665

KEYWORD

nonn,fini,base

AUTHOR

Hugo Pfoertner, Feb 28 2005

EXTENSIONS

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

Edited by Charles R Greathouse IV, Aug 03 2010

STATUS

approved

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Last modified July 19 09:33 EDT 2019. Contains 325155 sequences. (Running on oeis4.)