A133559 Primes which have a partition as the sum of squares of five consecutive primes.

373, 653, 5381, 6701, 8069, 19541, 24821, 53549, 56909, 69389, 93581, 107741, 131837, 184901, 196661, 237821, 252509, 344021, 370661, 395069, 498989, 609269, 783701, 1055429, 1174781, 1239341, 1492637, 1576229, 1713989, 1749149, 2024261

Offset

1,1

Comments

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

For sums of squares of three consecutive primes (A133529), it seems that only 83 belonging (checked for starting primes prime(k) for all k < 1000000).

Sums of squares of four (and all even numbers of) consecutive primes are even numbers with the exception of 2^2 + 3^2 + 5^2 + 7^2 = 87 = 3*29, which is not prime.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

a(1)=373 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. [Corrected by Jonathan Sondow, Nov 04 2015]

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, k]], {n, 1, 100}]; b
Select[Total/@Partition[Prime[Range[200]]^2, 5, 1], PrimeQ] (* Harvey P. Dale, Apr 07 2015 *)

Crossrefs

Cf. A133529, A133538, A133560.

Sequence in context: A182573 A142921 A263724 * A229499 A023313 A213301

Adjacent sequences: A133556 A133557 A133558 * A133560 A133561 A133562

Keyword

nonn

Author

Artur Jasinski, Sep 16 2007

Status

approved