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

1,1

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.

Links

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A171395 A069426 A093733 * A202445 A062045 A043515

Adjacent sequences: A133559 A133560 A133561 * A133563 A133564 A133565

Keyword

nonn

Author

Artur Jasinski, Sep 16 2007

Extensions

Edited by Michel Marcus, Jul 08 2018

Status

approved