A133560 -id:A133560 - cp's OEIS frontend

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

Artur Jasinski, Sep 16 2007

nonn

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.

			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]

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

Cf. A133529, A133538, A133560.

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 *)

A133562 Numbers which are the sum of the squares of seven consecutive primes.

Original entry on oeis.org

666, 1023, 1543, 2359, 3271, 4519, 6031, 7591, 9439, 11719, 14359, 17119, 20239, 23599, 27079, 31111, 35191, 39631, 45319, 51031, 56599, 62719, 68359, 74239, 82447, 90199, 98767, 107479, 118231, 129151, 141031, 151471, 162199, 173359

Offset: 1

Artur Jasinski, Sep 16 2007

nonn

For primes in this sequence see A133560.
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 it seems that only 83 is a prime (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.
For primes that are sums of squares of five consecutive primes see A133559.

			a(6) = 13^2 + 17^2 + 19^2 + 23^2 + 29^2 + 31^2 + 37^2 = 4519.

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Cf. A133529, A133538, A133558, A133559, A133560, A133561.

seq(add(ithprime(n+k)^2,k=0..6),n=1..35); # Muniru A Asiru, Jul 08 2018

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; AppendTo[b, k], {n, 1, 100}]; b
Total/@Partition[Prime[Range[40]]^2,7,1] (* Harvey P. Dale, Jan 01 2025 *)

Edited by Michel Marcus, Jul 08 2018

cp's OEIS Frontend

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

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