A074113 -id:A074113 - cp's OEIS frontend

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

Amarnath Murthy, Aug 27 2002

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.

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

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

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

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

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

A074114 Largest n-digit number of the form p^a*q^b... with the maximum value of a+b+.... where p, q etc. are primes.

Original entry on oeis.org

8, 96, 768, 8192, 98304, 786432, 8388608, 67108864, 805306368, 8589934592, 68719476736, 824633720832, 8796093022208, 70368744177664, 844424930131968, 9007199254740992, 72057594037927936, 864691128455135232, 9223372036854775808, 73786976294838206464

Offset: 1

Amarnath Murthy, Aug 27 2002

			a(2) = 96 = 2^5*3 a+b 5+1= 6 and is the maximum one can get with the largest two digit number 96.

Cf. A074113.

The elements of this sequence have the form 2^a*3^b where a is an integer and b is either 0 or 1. - Stefan Steinerberger, Nov 05 2005

If 2^(floor(log_2(10^n))) < (2/3)*10^n then a(n)=2^(floor(log_2(10^n)))*3, otherwise a(n) is 2^(floor(log_2(10^n))), where log_2 denotes the logarithm in base 2. - Stefan Steinerberger, Nov 15 2005

a(5)-a(14) from Stefan Steinerberger, Nov 15 2005

More terms from Sean A. Irvine, Jan 11 2025

cp's OEIS Frontend

A074116 Largest n-digit power of 2.

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