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A103662
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Smallest power with base>1 and exponent n whose decimal representation doesn't contain the digit 0.
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11
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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
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OFFSET
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0,2
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COMMENTS
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For statistical reasons it is conjectured that the sequence is finite.
a(40), if it exists, is not known.
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)
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LINKS
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FORMULA
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EXAMPLE
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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).
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PROG
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CROSSREFS
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Cf. A103663 = smallest bases x such that x^n has a zero-less decimal representation.
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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Keyword:fini removed by Jianing Song, Jan 28 2023 as finiteness is only conjectured.
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STATUS
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approved
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