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URL: https://oeis.org/A133557

⇱ A133557 - OEIS

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A133557
Numbers k for which the sum of squares of five consecutive primes starting with prime(k) is prime (A133559).
0
2, 3, 9, 10, 11, 16, 18, 25, 26, 28, 31, 33, 36, 42, 43, 46, 47, 54, 56, 58, 63, 68, 76, 87, 91, 93, 99, 101, 105, 106, 114, 127, 131, 145, 153, 159, 183, 186, 196, 201, 206, 229, 230, 232, 233, 238, 239, 241, 244, 245, 246, 248, 253, 256, 257, 264, 265, 266, 268
OFFSET
1,1
COMMENTS
For sums of squares of two consecutive primes, only k=1 yields a prime.
For sums of squares of three consecutive primes A133529, it seems that only k=2 yields a prime (checked for all k < 1000000).
Sums of squares of four (and all even numbers of) consecutive primes are even numbers except at k=1.
EXAMPLE
a(1)=2 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.
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, n]], {n, 1, 100}]; b (* Artur Jasinski *)
CROSSREFS
Sequence in context: A037463 A309348 A270886 * A047475 A376200 A291610
KEYWORD
nonn
AUTHOR
Artur Jasinski, Sep 16 2007
EXTENSIONS
Name and example corrected by Jonathan Sondow, Nov 04 2015
STATUS
approved