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A180306 a(n) is the largest integer k for which the Frobenius equation a_1*x_1 + a_2*x_2 + ... + a_n*x_n == k has no nonnegative integer solutions, where the a_i are consecutive primes beginning with the n-th prime. 2
1, 4, 9, 16, 27, 35, 49, 63, 65, 85, 95, 105, 121, 135, 145, 169, 175, 187, 203, 209, 221, 253, 265, 273, 289, 301, 305, 319, 351, 369, 387, 403, 407, 425, 445, 473, 485, 495, 517, 529, 545, 551, 567, 611, 615, 635, 639, 671, 679, 693, 703, 725, 747, 781, 793 (list; graph; refs; listen; history; text; internal format)
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

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

Cf. A007414.

Sequence in context: A266336 A027365 A100216 * A138994 A195618 A066969

Adjacent sequences:  A180303 A180304 A180305 * A180307 A180308 A180309

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, Aug 25 2010

EXTENSIONS

Edited by N. J. A. Sloane, Aug 26 2010

STATUS

approved

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Last modified October 18 23:08 EDT 2019. Contains 328211 sequences. (Running on oeis4.)