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A073497
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a(n) = n^2 - prime(n).
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4
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-1, 1, 4, 9, 14, 23, 32, 45, 58, 71, 90, 107, 128, 153, 178, 203, 230, 263, 294, 329, 368, 405, 446, 487, 528, 575, 626, 677, 732, 787, 834, 893, 952, 1017, 1076, 1145, 1212, 1281, 1354, 1427, 1502, 1583, 1658, 1743, 1828, 1917, 1998, 2081, 2174, 2271, 2368
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OFFSET
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1,3
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COMMENTS
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a(n) is never a perfect square for n>=5. [Proof: assume on the contrary n^2 - prime(n) = k^2, equivalent to (n+k)*(n-k) = prime(n). Since prime(n) cannot be the product of two nontrivial factors, this equation can only hold for k=n-1, i.e., prime(n)=2n-1. This contradicts the assumption and completes the proof.] - Alexander R. Povolotsky, Oct 01 2008
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LINKS
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MATHEMATICA
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Table[n^2 - Prime[n], {n, 1, 55}]
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PROG
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(PARI) for(n=1, 51, print1(n*n-prime(n), ", "))
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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