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

1,1

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.

Links

Table of n, a(n) for n=1..59.

Example

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.

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 *)

Crossrefs

Cf. A133538, A133559.

Sequence in context: A037463 A309348 A270886 * A047475 A291610 A285428

Adjacent sequences: A133554 A133555 A133556 * A133558 A133559 A133560

Keyword

nonn

Author

Artur Jasinski, Sep 16 2007

Extensions

Name and example corrected by Jonathan Sondow, Nov 04 2015

Status

approved