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A275747 Largest integer which cannot be written as a sum of n-th powers of odd primes. 3
4, 114, 1595, 24195, 190463, 4613167, 23815950, 240951477, 2448240688, 40379465440, 258630935725, 3044619003271, 26232953378021, 264066033166293, 3218396161633945, 29248021240625765, 302064442857973298, 3027736057187540859, 32207709908667683204 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
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
LINKS
H. Greenberg, Solution to a linear diophantine equation for nonnegative integers, Journal of Algorithms, 9 (1988), 343-353.
EXAMPLE
For n=2, 114 is the largest integer which cannot be written as a sum of squares of odd primes.
MATHEMATICA
With[{prs=Prime[Range[2, 5]]}, Table[FrobeniusNumber[prs^n], {n, 20}]] (* Harvey P. Dale, Sep 19 2018 *)
CROSSREFS
Cf. A275746. For all primes, including 2, see A275743, A122615.
Sequence in context: A199834 A194495 A260575 * A239942 A261457 A080482
KEYWORD
nonn
AUTHOR
Mike Oakes, Aug 07 2016
STATUS
approved

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Last modified May 29 13:49 EDT 2024. Contains 372948 sequences. (Running on oeis4.)