cp's OEIS Frontend

A129389 Numbers k such that the mean of 5 consecutive squares starting with k^2 is prime.

%I A129389 #27 Aug 01 2025 17:05:08
%S A129389 1,7,13,19,31,37,43,55,79,97,103,109,115,121,145,169,217,223,235,241,
%T A129389 247,253,271,295,301,307,319,343,349,361,367,373,385,415,421,427,439,
%U A129389 445,451,475,499,511,547,553,559,571,601,607,649,673,679,697,709,751
%N A129389 Numbers k such that the mean of 5 consecutive squares starting with k^2 is prime.
%C A129389 Sum of 5 consecutive squares starting with k^2 is equal to 5*(6 + 4*k + k^2) and mean is (6 + 4*k + k^2) = (k+2)^2 + 2. Hence a(n) = A067201(n+2).
%C A129389 Also, numbers k such that A000217(k) + A000217(k+3) is prime. - _Bruno Berselli_, Apr 17 2013
%H A129389 Bruno Berselli, <a href="/A129389/b129389.txt">Table of n, a(n) for n = 1..1000</a>
%e A129389 (1^2 + ... + 5^2)/5 = 11, which is prime;
%e A129389 (7^2 + ... + 11^2)/5 = 83, which is prime;
%e A129389 (13^2 + ... + 17^2)/5 = 227, which is prime.
%t A129389 Select[Range[800], PrimeQ[#^2 + 4 # + 6] &] (* _Bruno Berselli_, Apr 17 2012 *)
%o A129389 (Magma) [n: n in [1..800] | IsPrime(n^2+4*n+6)]; /* or, from the second comment: */ A000217:=func<i | i*(i+1) div 2>; [n: n in [1..800] | IsPrime(A000217(n)+A000217(n+3))]; // _Bruno Berselli_, Apr 17 2013
%o A129389 (SageMath) [n for n in (1..1000) if is_prime(n^2+4*n+6)] # _G. C. Greubel_, Feb 04 2024
%Y A129389 Cf. A056899, A067201, A129388.
%Y A129389 Cf. A000217, A128815 (numbers n such that A000217(n)+A000217(n+2) is prime). [_Bruno Berselli_, Apr 17 2013]
%K A129389 nonn
%O A129389 1,2
%A A129389 _Zak Seidov_, Apr 12 2007