cp's OEIS Frontend

A133562 Numbers which are the sum of the squares of seven consecutive primes.

%I A133562 #22 Jun 08 2025 03:34:32
%S A133562 666,1023,1543,2359,3271,4519,6031,7591,9439,11719,14359,17119,20239,
%T A133562 23599,27079,31111,35191,39631,45319,51031,56599,62719,68359,74239,
%U A133562 82447,90199,98767,107479,118231,129151,141031,151471,162199,173359
%N A133562 Numbers which are the sum of the squares of seven consecutive primes.
%C A133562 For primes in this sequence see A133560.
%C A133562 For sum of squares of two consecutive primes only 2^2 + 3^2 = 13 is prime.
%C A133562 For sum of squares of three consecutive primes A133529 it seems that only 83 is a prime (checked for all n < 1000000).
%C A133562 Sums of squares of four (and all even number) of consecutive primes are even numbers with exception n=1 but 2^2 + 3^2 + 5^2 + 7^2 = 87 = 3*29 is not prime.
%C A133562 For primes that are sums of squares of five consecutive primes see A133559.
%H A133562 Seiichi Manyama, <a href="/A133562/b133562.txt">Table of n, a(n) for n = 1..10000</a>
%e A133562 a(6) = 13^2 + 17^2 + 19^2 + 23^2 + 29^2 + 31^2 + 37^2 = 4519.
%p A133562 seq(add(ithprime(n+k)^2,k=0..6),n=1..35); # _Muniru A Asiru_, Jul 08 2018
%t A133562 b = {}; a = 2; Do[k = Prime[n]^a + Prime[n + 1]^a + Prime[n + 2]^a + Prime[n + 3]^a + Prime[n + 4]^a + Prime[n + 5]^a + Prime[n + 6]^a; AppendTo[b, k], {n, 1, 100}]; b
%t A133562 Total/@Partition[Prime[Range[40]]^2,7,1] (* _Harvey P. Dale_, Jan 01 2025 *)
%Y A133562 Cf. A133529, A133538, A133558, A133559, A133560, A133561.
%K A133562 nonn
%O A133562 1,1
%A A133562 _Artur Jasinski_, Sep 16 2007
%E A133562 Edited by _Michel Marcus_, Jul 08 2018