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A112670
Smallest positive integer that has a different number of digits in each of the bases 2 through n.
3
1, 2, 9, 81, 1024, 16384, 1953125, 362797056, 96889010407, 281474976710656, 150094635296999121, 109418989131512359209, 1000000000000000000000000, 13109994191499930367061460371, 19781359483314150527412524285952, 442779263776840698304313192148785281
OFFSET
2,2
COMMENTS
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.)
REFERENCES
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
FORMULA
a(n) >> n^n. For any A < n, a(n) > exp(1/(1/log(n-A-1) - 1/log(n))). - Charles R Greathouse IV, May 01 2012
EXAMPLE
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.
CROSSREFS
KEYWORD
nonn,base
AUTHOR
N. J. A. Sloane, Dec 30 2005
STATUS
approved