A133557 Numbers k for which the sum of squares of five consecutive primes starting with prime(k) is prime (A133559).

2, 3, 9, 10, 11, 16, 18, 25, 26, 28, 31, 33, 36, 42, 43, 46, 47, 54, 56, 58, 63, 68, 76, 87, 91, 93, 99, 101, 105, 106, 114, 127, 131, 145, 153, 159, 183, 186, 196, 201, 206, 229, 230, 232, 233, 238, 239, 241, 244, 245, 246, 248, 253, 256, 257, 264, 265, 266, 268

Offset: 1

Author

Artur Jasinski, Sep 16 2007

Keywords

• nonn

Comments

For sums of squares of two consecutive primes, only k=1 yields a prime.

For sums of squares of three consecutive primes A133529, it seems that only k=2 yields a prime (checked for all k < 1000000).

Sums of squares of four (and all even numbers of) consecutive primes are even numbers except at k=1.

Examples

			a(1)=2 because prime(2)^2 + prime(3)^2 + prime(4)^2 + prime(5)^2 + prime(6)^2 = 3^2 + 5^2 + 7^2 + 11^2 + 13^2 = 373 is prime.
		

Crossrefs

Cf. A133538, A133559.

Programs

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; If[PrimeQ[k], AppendTo[b, n]], {n, 1, 100}]; b (* Artur Jasinski *)

Extensions

Name and example corrected by Jonathan Sondow, Nov 04 2015