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Search: id:A103662
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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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+0
2
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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, 33554432, 2541865828329, 134217728, 268435456, 36845653286788892983296, 931322574615478515625, 2147483648, 4294967296, 8589934592, 17179869184, 34359738368, 68719476736, 137438953472, 75557863725914323419136, 549755813888
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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For statistical reasons it is conjectured that the sequence is finite.
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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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CROSSREFS
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Cf. A103663 = smallest bases x such that x^n has a zero-less decimal representation.
Sequence in context: A120617 A050732 A138815 this_sequence A023423 A079838 A109912
Adjacent sequences: A103659 A103660 A103661 this_sequence A103663 A103664 A103665
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KEYWORD
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nonn,fini
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AUTHOR
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Hugo Pfoertner (hugo(AT)pfoertner.org), Feb 28 2005
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EXTENSIONS
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a(21)=381^21 found by Joshua Zucker (joshua.zucker(AT)stanfordalumni.org). For statistical reasons it is conjectured that the sequence is finite.
a(40), if it exists, is not known.
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