|
|
A133559
|
|
Primes which have a partition as the sum of squares of five consecutive primes.
|
|
6
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|