OFFSET
1,2
COMMENTS
Many terms are squares, their square roots being 1, 2, 3, 4, 7, 11, 13, 17, 23, 35, 37, 59, 69, 79, 89, 101, 103, ..., .
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..2000
Michael Hellus, Anton Rechenauer, Rolf Waldi, Numerical Semigroups generated by Primes, arXiv:1908.09483 [math.NT], 2019.
FORMULA
2p-2 <= a(n) << p^2, where p is the n-th prime, for n > 1. - Charles R Greathouse IV, Apr 03 2012
a(n) <= A007414(n), so conjecturally a(n) ~ 3*prime(n). - Charles R Greathouse IV, Apr 03 2012
MATHEMATICA
f[n_] := FrobeniusNumber[ Prime@ Range[n, n + 100]]; Array[f, 55]
FrobeniusNumber/@Partition[Prime[Range[300]], 100, 1] (* Harvey P. Dale, Jun 01 2017 *)
PROG
(PARI) issum(n, x)=if(isprime(n), return(n>=x)); if(if(n%2, n<3*x, n<2*x), return(!n)); forprime(p=x, n-if(n%2, 2*x, x), if(issum(n-p, p), return(1))); 0
a(n)=if(n<2, return(1)); my(p=prime(n), k=2*p-2, lower=k, upper=2*k+2); while(upper>lower, if(issum(upper, p), upper--, lower=2*k+2; k=upper; upper=2*k+2)); k \\ Charles R Greathouse IV, Apr 03 2012
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Aug 25 2010
EXTENSIONS
Edited by N. J. A. Sloane, Aug 26 2010
STATUS
approved