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.

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

Offset

1,1

Links

Table of n, a(n) for n=1..20.

Formula

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

Example

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.

Crossrefs

Cf. A074113.

Sequence in context: A229294 A241813 A116144 * A069650 A066424 A276593

Adjacent sequences: A074111 A074112 A074113 * A074115 A074116 A074117

Keyword

base,nonn

Author

Amarnath Murthy, Aug 27 2002

Extensions

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

More terms from Sean A. Irvine, Jan 11 2025

Status

approved