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 A073497 a(n) = n^2 - prime(n). 3
 -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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS 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 LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 MATHEMATICA Table[n^2 - Prime[n], {n, 1, 55}] PROG (PARI) for(n=1, 51, print1(n*n-prime(n), ", ")) (MAGMA) [n^2 - NthPrime(n): n in [1..100] ]; // Vincenzo Librandi, Apr 12 2011 CROSSREFS Sequence in context: A099980 A281314 A004630 * A244941 A086192 A105503 Adjacent sequences:  A073494 A073495 A073496 * A073498 A073499 A073500 KEYWORD sign,easy AUTHOR Werner D. Sand, Aug 27 2002 EXTENSIONS More terms from Klaus Brockhaus and Robert G. Wilson v, Aug 28 2002 STATUS approved

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Last modified July 3 10:25 EDT 2022. Contains 355050 sequences. (Running on oeis4.)