cp's OEIS Frontend

A133560 Primes which have a partition as the sum of squares of seven consecutive primes.

%I A133560 #25 Sep 04 2023 22:53:06
%S A133560 1543,3271,4519,7591,9439,11719,23599,39631,45319,51031,56599,90199,
%T A133560 151471,173359,210319,222919,235159,261463,313879,367711,402511,
%U A133560 459223,478831,499711,610567,634327,732967,760519,819319,883087,939439,968959
%N A133560 Primes which have a partition as the sum of squares of seven consecutive primes.
%C A133560 For sums of squares of two consecutive primes, only 2^2 + 3^2 = 13 is prime.
%C A133560 For sums of squares of three consecutive primes (see A133529), it seems that only 3^2 + 5^2 + 7^2 = 83 is prime.
%C A133560 Sums of squares of four (and all even numbers of) consecutive primes are even numbers except for 2^2 + 3^2 + 5^2 + 7^2 = 87 = 3*29, which is not prime.
%C A133560 For sums of squares of five of consecutive primes see A133559.
%C A133560 For every prime p > 3, p^2 mod 3 = 1, so the sum of the squares of any 3 such primes will be divisible by 3. - _Jon E. Schoenfield_, Sep 04 2023
%H A133560 Muniru A Asiru, <a href="/A133560/b133560.txt">Table of n, a(n) for n = 1..3000</a>
%e A133560 a(3)=4519 because 13^2 + 17^2 + 19^2 + 23^2 + 29^2 + 31^2 + 37^2 = 4519 is prime.
%p A133560 select(isprime,[seq(add(ithprime(n+k)^2,k=0..6),n=1..80)]); # _Muniru A Asiru_, Jul 19 2018
%t A133560 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; If[PrimeQ[k], AppendTo[b, k]], {n, 1, 100}]; b
%t A133560 (* Second program: *)
%t A133560 Select[Map[Total, Partition[Prime@ Range@ 80, 7, 1]^2], PrimeQ] (* _Michael De Vlieger_, Jul 20 2018 *)
%Y A133560 Cf. A133529, A133538, A133559, A133561.
%K A133560 nonn
%O A133560 1,1
%A A133560 _Artur Jasinski_, Sep 16 2007