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 A129389 Numbers n such that the mean of 5 consecutive squares starting with n^2 is prime. 4
 1, 7, 13, 19, 31, 37, 43, 55, 79, 97, 103, 109, 115, 121, 145, 169, 217, 223, 235, 241, 247, 253, 271, 295, 301, 307, 319, 343, 349, 361, 367, 373, 385, 415, 421, 427, 439, 445, 451, 475, 499, 511, 547, 553, 559, 571, 601, 607, 649, 673, 679, 697, 709, 751 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Sum of 5 consecutive squares starting with n^2 is equal to 5*(6 + 4*n + n^2) and mean is (6 + 4*n + n^2) = (n+2)^2 + 2. Hence a(n) = A067201(n+2). Also, numbers n such that A000217(n) + A000217(n+3) is prime. - Bruno Berselli, Apr 17 2013 LINKS Bruno Berselli, Table of n, a(n) for n = 1..1000 EXAMPLE (1^2 + ... + 5^2)/5 = 11, which is prime; (7^2 + ... + 11^2)/5 = 83, which is prime; (13^2 + ... + 17^2)/5 = 227, which is prime. MATHEMATICA Select[Range[800], PrimeQ[#^2 + 4 # + 6] &] (* Bruno Berselli, Apr 17 2012 *) PROG (Magma) [n: n in [1..800] | IsPrime(n^2+4*n+6)]; /* or, from the second comment: */ A000217:=func; [n: n in [1..800] | IsPrime(A000217(n)+A000217(n+3))]; // Bruno Berselli, Apr 17 2013 (SageMath) [n for n in (1..1000) if is_prime(n^2+4*n+6)] # G. C. Greubel, Feb 04 2024 CROSSREFS Cf. A056899, A067201, A129388. Cf. A000217, A128815 (numbers n such that A000217(n)+A000217(n+2) is prime). [Bruno Berselli, Apr 17 2013] Sequence in context: A133290 A038590 A218146 * A107925 A002476 A123365 Adjacent sequences: A129386 A129387 A129388 * A129390 A129391 A129392 KEYWORD nonn AUTHOR Zak Seidov, Apr 12 2007 STATUS approved

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Last modified September 12 07:57 EDT 2024. Contains 375850 sequences. (Running on oeis4.)