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

666, 1023, 1543, 2359, 3271, 4519, 6031, 7591, 9439, 11719, 14359, 17119, 20239, 23599, 27079, 31111, 35191, 39631, 45319, 51031, 56599, 62719, 68359, 74239, 82447, 90199, 98767, 107479, 118231, 129151, 141031, 151471, 162199, 173359

Offset: 1

Author

Artur Jasinski, Sep 16 2007

Keywords

• nonn

Comments

For primes in this sequence see A133560.

For sum of squares of two consecutive primes only 2^2 + 3^2 = 13 is prime.

For sum of squares of three consecutive primes A133529 it seems that only 83 is a prime (checked for all n < 1000000).

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.

For primes that are sums of squares of five consecutive primes see A133559.

Examples

			a(6) = 13^2 + 17^2 + 19^2 + 23^2 + 29^2 + 31^2 + 37^2 = 4519.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A133529, A133538, A133558, A133559, A133560, A133561.

Programs

Maple

seq(add(ithprime(n+k)^2,k=0..6),n=1..35); # Muniru A Asiru, Jul 08 2018

Mathematica

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
Total/@Partition[Prime[Range[40]]^2,7,1] (* Harvey P. Dale, Jan 01 2025 *)

Extensions

Edited by Michel Marcus, Jul 08 2018