A112670 Smallest positive integer that has a different number of digits in each of the bases 2 through n.

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

Links

Table of n, a(n) for n=2..17.

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

Cf. A112671, A112672, A112673.

Sequence in context: A212271 A147302 A301861 * A117581 A110567 A123570

Adjacent sequences: A112667 A112668 A112669 * A112671 A112672 A112673

Keyword

nonn,base

Author

N. J. A. Sloane, Dec 30 2005

Status

approved