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%I #19 Mar 05 2020 03:14:25
%S 5,11,19,23,37,41,53,59,83,89,113,131,167,173,179,229,251,269,293,313,
%T 317,383,389,439,443,509,599,641,683,859,929,1031,1033,1049,1163,1193,
%U 1283,1301,1303,1307,1439,1493,1499,1543,1619,1733,2143,2153,2333,2687,2693,3083,3089,3533,3719,3989,4003,4583,4673,4703,5387,5651,5849,5903,6173,6389,6449,7481,9293,12113,15803,16433,19763,61403
%N Primes that are not the sum of 3 hexagonal numbers.
%D Legendre, Théorie des Nombres, 3rd edition, 1830.
%H W. Duke and R. Schulze-Pilot, <a href="http://gdz.sub.uni-goettingen.de/dms/load/img/?PID=GDZPPN002107066">Representation of integers by positive ternary quadratic forms and equidistribution of lattice points on ellipsoids</a>, Invent. Math. 99(1990), 49-57.
%H R. K. Guy, <a href="http://www.jstor.org/stable/2324367">Every number is expressible as the sum of how many polygonal numbers?</a>, Amer. Math. Monthly 101 (1994), 169-172.
%F A000040 INTERSECT A007536.
%e 5 is the sum of five hexagonal numbers; 11 is the sum of six hexagonal numbers; the other 72 primes are the sum of four hexagonal numbers. - _T. D. Noe_, Apr 20 2006
%t nn=201; hex=Table[n(2n-1), {n,0,nn-1}]; ps=Prime[Range[PrimePi[hex[[ -1]]]]]; Do[n=hex[[i]]+hex[[j]]+hex[[k]]; If[n<=hex[[ -1]]&&PrimeQ[n], ps=DeleteCases[ps,n]], {i,nn}, {j,i,nn}, {k,j,nn}]; ps (* _T. D. Noe_, Apr 20 2006 *)
%Y Cf. A000040, A000384, A007527, A007536, A117065.
%K easy,fini,nonn
%O 1,1
%A _Jonathan Vos Post_, Apr 18 2006
%E More terms from _T. D. Noe_, who conjectures that the list shown here is complete. His search up to 7*10^7 gave no further terms. - Apr 20 2006