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Search: id:A014090
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| A014090 |
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Numbers that are not the sum of a square and a prime. |
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+0
5
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| 1, 10, 25, 34, 58, 64, 85, 91, 121, 130, 169, 196, 214, 226, 289, 324, 370, 400, 526, 529, 625, 676, 706, 730, 771, 784, 841, 1024, 1089, 1225, 1255, 1351, 1414, 1444, 1521, 1681, 1849, 1906, 1936, 2116, 2209, 2304, 2500, 2809, 2986, 3136, 3364, 3481, 3600
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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
21679 is the last known non-square in this sequence. See A020495. - T. D. Noe (noe(AT)sspectra.com), Aug 05 2006
A002471(a(n))=0; complement of A014089. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Sep 07 2008]
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..115
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MATHEMATICA
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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
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CROSSREFS
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A064233. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Sep 07 2008]
Sequence in context: A057462 A048195 A133634 this_sequence A154057 A074814 A002600
Adjacent sequences: A014087 A014088 A014089 this_sequence A014091 A014092 A014093
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), R. K. Guy
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