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A064233
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Numbers that are not the sum of a prime number and a nonzero square.
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8
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1, 2, 5, 10, 13, 25, 31, 34, 37, 58, 61, 64, 85, 91, 121, 127, 130, 169, 196, 214, 226, 289, 324, 370, 379, 400, 439, 526, 529, 571, 625, 676, 706, 730, 771, 784, 829, 841, 991, 1024, 1089, 1225, 1255, 1351, 1414, 1444, 1521, 1549, 1681, 1849, 1906, 1936, 2116
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OFFSET
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1,2
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COMMENTS
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LINKS
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EXAMPLE
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5 = 1+4 or 2+3; a prime and a square do not appear together in either sum.
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MATHEMATICA
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Complement[ Table[ n, {n, 1, 10000} ], Union[ Flatten[ Table[ Prime[ i ] + j^2, {i, 1, 1230}, {j, 1, 100} ] ] ] ]
nspQ[n_]:=Length[Select[IntegerPartitions[n, {2}], (PrimeQ[#[[1]]] && IntegerQ[ Sqrt[ #[[2]]]])||(PrimeQ[#[[2]]]&&IntegerQ[Sqrt[#[[1]]]])&]] == 0; Select[ Range[ 2200], nspQ] (* Harvey P. Dale, Jun 18 2021 *)
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PROG
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(PARI) list(lim)=my(v=vectorsmall(lim\1, i, 1), u=List(), b); forprime(p=2, #v, b=0; while((t=p+b++^2)<=#v, v[t]=0)); for(i=1, #v, if(v[i], listput(u, i))); Vec(u) \\ Charles R Greathouse IV, May 29 2012
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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