A074116 Largest n-digit power of 2.

8, 64, 512, 8192, 65536, 524288, 8388608, 67108864, 536870912, 8589934592, 68719476736, 549755813888, 8796093022208, 70368744177664, 562949953421312, 9007199254740992, 72057594037927936, 576460752303423488, 9223372036854775808, 73786976294838206464, 590295810358705651712

Offset: 1

Author

Amarnath Murthy, Aug 27 2002

Keywords

• base
• nonn

Comments

The exponents are given in A066343. - Evgeny Kapun, Jan 16 2017

An equivalent definition (which was formerly the definition of A074113): "Smallest n-digit number of the form p^a*q^b... with the maximum value of a+b+.... where p, q etc. are primes. If a,b,c,... are the indices in the signature prime factorization then a+b+c ... is a maximum." That this is the same sequence follows from the inequality p^a*q^b... >= 2^(a+b+...) and the fact that there always exists a power of 2 between two consecutive powers of 10.

Links

• Evgeny Kapun, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A066343, A067488, A074113, A074114, A074117, A074118.

Programs

Mathematica

Last[#]&/@(With[{l2=2^Range[80]},Table[Select[l2,IntegerLength[#] == n&], {n,22}]]) (* Harvey P. Dale, Jul 17 2011 *)

Formula

a(n) = 2^A066343(n).

Extensions

Edited by R. J. Mathar, Feb 13 2008, Max Alekseyev, Mar 10 2009, Harvey P. Dale, Jul 17 2011, Evgeny Kapun, Jan 16 2017, and N. J. A. Sloane, Jan 18 2017