Search: id:A014090
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%I A014090
%S A014090 1,10,25,34,58,64,85,91,121,130,169,196,214,226,289,324,370,400,526,529,
%T A014090 625,676,706,730,771,784,841,1024,1089,1225,1255,1351,1414,1444,1521,
%U A014090 1681,1849,1906,1936,2116,2209,2304,2500,2809,2986,3136,3364,3481,3600
%N A014090 Numbers that are not the sum of a square and a prime.
%C A014090 Sequence is infinite: if 2n-1 is composite then n^2 is in the sequence. 
               (Proof: If n^2 = x^2 + p with p prime, then p = (n-x)(n+x), so n-x=1 
               and n+x=p. Hence 2n-1=p is prime, not composite.) - Dean Hickerson, 
               Nov 27, 2002
%C A014090 21679 is the last known non-square in this sequence. See A020495. - T. 
               D. Noe (noe(AT)sspectra.com), Aug 05 2006
%C A014090 A002471(a(n))=0; complement of A014089. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Sep 07 2008]
%H A014090 T. D. Noe, <a href="b014090.txt">Table of n, a(n) for n = 1..115</a>
%t A014090 t={}; Do[k=0; While[k^2<n && !PrimeQ[n-k^2], k++ ]; If[k^2>=n, AppendTo[t,
               n]], {n,25000}]; t - T. D. Noe (noe(AT)sspectra.com), Aug 05 2006
%Y A014090 A064233. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Sep 07 2008]
%Y A014090 Sequence in context: A057462 A048195 A133634 this_sequence A154057 A074814 
               A002600
%Y A014090 Adjacent sequences: A014087 A014088 A014089 this_sequence A014091 A014092 
               A014093
%K A014090 nonn,easy,nice
%O A014090 1,2
%A A014090 N. J. A. Sloane (njas(AT)research.att.com), R. K. Guy

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