A070327 Smallest nontrivial power of n starting with n and greater than n.

256, 387420489, 4096, 59604644775390625, 60466176, 79792266297612001, 8589934592, 984770902183611232881, 100, 1191817653772720942460132761, 1283918464548864, 137858491849, 1475789056

Offset: 2

Author

Amarnath Murthy, May 11 2002

Keywords

• base
• nonn

Comments

a(n) = n ^ A051248(n). - Reinhard Zumkeller, Sep 29 2011

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 2..32

Crossrefs

Cf. A045537, A104782.

Programs

Python

from itertools import count
def a(n):
    s = str(n)
    return next(n**e for e in count(2) if str(n**e).startswith(s))
print([a(n) for n in range(2, 16)]) # Michael S. Branicky, Feb 23 2025

Formula

f[n_] := Block[{k = 2, s = ToString[n]}, While[ StringPosition[ ToString[n^k], s, 1] != {{1, Integer_}}, k++ ]; n^k]; Table[ f[n], {n, 2, 10}]

Extensions

Edited by Robert G. Wilson v, May 14 2002

The 15th term is too large to include.