A133560 Primes which have a partition as the sum of squares of seven consecutive primes.

1543, 3271, 4519, 7591, 9439, 11719, 23599, 39631, 45319, 51031, 56599, 90199, 151471, 173359, 210319, 222919, 235159, 261463, 313879, 367711, 402511, 459223, 478831, 499711, 610567, 634327, 732967, 760519, 819319, 883087, 939439, 968959

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 (see A133529), it seems that only 3^2 + 5^2 + 7^2 = 83 is prime.

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

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

For every prime p > 3, p^2 mod 3 = 1, so the sum of the squares of any 3 such primes will be divisible by 3. - Jon E. Schoenfield, Sep 04 2023

Links

Muniru A Asiru, Table of n, a(n) for n = 1..3000

Example

a(3)=4519 because 13^2 + 17^2 + 19^2 + 23^2 + 29^2 + 31^2 + 37^2 = 4519 is prime.

Maple

select(isprime, [seq(add(ithprime(n+k)^2, k=0..6), n=1..80)]); # Muniru A Asiru, Jul 19 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; If[PrimeQ[k], AppendTo[b, k]], {n, 1, 100}]; b
(* Second program: *)
Select[Map[Total, Partition[Prime@ Range@ 80, 7, 1]^2], PrimeQ] (* Michael De Vlieger, Jul 20 2018 *)

Crossrefs

Cf. A133529, A133538, A133559, A133561.

Sequence in context: A375490 A137598 A252966 * A232102 A234031 A038009

Adjacent sequences: A133557 A133558 A133559 * A133561 A133562 A133563

Keyword

nonn

Author

Artur Jasinski, Sep 16 2007

Status

approved