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