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%I #17 Jan 27 2023 13:35:23
%S 1,4,9,16,27,35,49,63,102,114,138,150,162,221,257,275,352,368,398,424,
%T 452,559,686,633,772,705,723,747,777,938,1149,1189,1231,1406,1637,
%U 1536,1741,1799,2193,1913,1967,1824,2099,2125,2165,2438,2769,3347,3403,3212
%N a(n) = Frobenius number for 8 successive primes = F[p(n), p(n+1), p(n+2), p(n+3), p(n+4), p(n+5), p(n+6), p(n+7)].
%e a(4)=16 because 16 is the largest number k such that the equation 7*x_1 + 11*x_2 + 13*x_3 + 17*x_4 + 19*x_5 + 23*x_6 + 29*x_7 + 31*x_8 = k has no solution for any nonnegative x_i (in other words, for every k > 16 there exist one or more solutions).
%t Table[FrobeniusNumber[{Prime[n],Prime[n + 1], Prime[n + 2], Prime[n + 3], Prime[n + 4], Prime[n + 5], Prime[n + 6], Prime[n + 7]}], {n, 1, 100}]
%t FrobeniusNumber/@Partition[Prime[Range[100]],8,1] (* _Harvey P. Dale_, Aug 15 2014 *)
%Y Frobenius numbers for k successive primes: A037165 (k=2), A138989 (k=3), A138990 (k=4), A138991 (k=5), A138992 (k=6), A138993 (k=7), this sequence (k=8).
%Y Cf. A028387, A079326, A138985, A138986, A138987, A138988.
%K nonn
%O 1,2
%A _Artur Jasinski_, Apr 05 2008