A275747 Largest integer which cannot be written as a sum of n-th powers of odd primes.

4, 114, 1595, 24195, 190463, 4613167, 23815950, 240951477, 2448240688, 40379465440, 258630935725, 3044619003271, 26232953378021, 264066033166293, 3218396161633945, 29248021240625765, 302064442857973298, 3027736057187540859, 32207709908667683204

Offset: 1

Author

Mike Oakes, Aug 07 2016

Keywords

• nonn

Comments

Except for n=6, only the powers of 3 primes are needed, namely 3^n, 5^n and 7^n, which leads to an ultra-fast O(n) execution time. I executed the algorithm in Greenberg (1988) with a PARI/GP program in only a few seconds for 1000 terms. - Mike Oakes, Aug 16 2016

Examples

			For n=2, 114 is the largest integer which cannot be written as a sum of squares of odd primes.
		

Links

• Mike Oakes, Table of n, a(n) for n = 1..1000
• H. Greenberg, Solution to a linear diophantine equation for nonnegative integers, Journal of Algorithms, 9 (1988), 343-353.

Crossrefs

Cf. A275746. For all primes, including 2, see A275743, A122615.

Programs

Mathematica

With[{prs=Prime[Range[2,5]]},Table[FrobeniusNumber[prs^n],{n,20}]] (* Harvey P. Dale, Sep 19 2018 *)