A133561 Numbers n for which sum of squares of seven consecutive primes(n,n+1,n+2,n+3,n+4,n+5,n+6) is prime.

3, 5, 6, 8, 9, 10, 14, 18, 19, 20, 21, 26, 32, 34, 37, 38, 39, 41, 44, 47, 49, 52, 53, 54, 59, 60, 63, 64, 66, 68, 70, 71, 75, 83, 88, 89, 91, 92, 97, 100, 107, 108, 110, 112, 113, 117, 122, 125, 128, 129, 131, 135, 141, 142, 150, 151, 157, 158, 165, 168, 169, 178, 183

Offset: 1

Author

Artur Jasinski, Sep 16 2007

Keywords

• nonn

Comments

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 seems that only 83 belonging (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.

Sums of squares of five of consecutive primes A133559.

Sums of squares of seven of consecutive primes A133562.

Examples

			a(3)=6 because prime(6)^2+prime(7)^2+prime(8)^2+prime(9)^2+prime(10)^2+prime(11)^2+prime(12)^2 = 13^2+17^2+19^2+23^2+29^2+31^2+37^2=4519 is prime.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A133538, A133559, A133562.

Programs

Maple

select(n->isprime(add(ithprime(n+k)^2,k=0..6)),[$1..200]); # Muniru A Asiru, Jul 28 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, n]], {n, 1, 100}]; b

PARI

is(n) = ispseudoprime(sum(i=0, 6, prime(n+i)^2)) \\ Felix Fröhlich, Jul 28 2018