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Search: id:A112670
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| A112670 |
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Smallest positive integer that has a different number of digits in each of the bases 2 through n. |
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+0
4
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| 1, 2, 9, 81, 1024, 16384, 1953125, 362797056, 96889010407, 281474976710656, 150094635296999121, 109418989131512359209, 1000000000000000000000000, 13109994191499930367061460371, 19781359483314150527412524285952, 442779263776840698304313192148785281
(list; graph; listen)
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OFFSET
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2,2
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COMMENT
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Comment from Jack Brennan: The base of each member seems to be roughly n-O(log n*log log n). The exponent of each member seems to be roughly n*O(log n). The sequence of bases seems to only have differences of +1 or 0. The sequence of exponents seems to only have positive differences.
Does 120 ever appear as a base? (See A112672.)
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REFERENCES
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David W. Wilson, Posting to Sequence Fan mailing list, Dec 28 2005
Jack Brennen computed the first 100 terms. Posting to Sequence Fan mailing list, Dec 28 2005
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EXAMPLE
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The sequence begins 2^0, 2^1, 3^2, 3^4, 4^5, 4^7, 5^9, 6^11, 7^13, 8^16, 9^18, 9^21, 10^24, 11^27, 12^29, 13^32, 14^35, 14^39, 15^42, 16^45, .... The bases and exponents are in A112672 and A112671 respectively.
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CROSSREFS
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Cf. A112671, A112672, A112673.
Sequence in context: A109519 A135868 A147302 this_sequence A117581 A123570 A006040
Adjacent sequences: A112667 A112668 A112669 this_sequence A112671 A112672 A112673
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Dec 30 2005
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