A133529 Sum of squares of three consecutive primes.

38, 83, 195, 339, 579, 819, 1179, 1731, 2331, 3171, 4011, 4899, 5739, 6867, 8499, 10011, 11691, 13251, 14859, 16611, 18459, 21051, 24219, 27531, 30219, 32259, 33939, 36099, 40779, 46059, 52059, 55251, 60291, 64323, 69651, 74019, 79107, 84387, 89859, 94731, 101283

Offset

1,1

Comments

It is easy to see that all terms > 83 are divisible by 3.

Likewise all terms except 38 are congruent to 3 (mod 8). - Franklin T. Adams-Watters, Jun 17 2015

Links

K. D. Bajpai, Table of n, a(n) for n = 1..10000

Formula

a(n) = A069484(n) + A001248(n+2). - Michel Marcus, Nov 08 2013

Example

a(1)=38 because 2^2 + 3^2 + 5^2 = 38.

Mathematica

a = 2; Table[Prime[n]^a + Prime[n + 1]^a + Prime[n + 2]^a, {n, 1, 100}]
Total/@Partition[Prime[Range[50]]^2, 3, 1] (* Vincenzo Librandi, Jun 18 2015 *)

Prog

(PARI)  for( n= 1, 100,  k= sum(i=n, n+2, prime(i)^2) ; print1(k, ", ")) \\ K. D. Bajpai, Jun 17 2015
(Magma)  [&+[ NthPrime(n+i)^2 :  i in [0..2]] : n in [1..20]]; // K. D. Bajpai, Jun 17 2015

Crossrefs

Cf. A034963, A133524-A133528, A133530-A133533.

Sequence in context: A039421 A043244 A044024 * A211498 A244733 A044176

Adjacent sequences: A133526 A133527 A133528 * A133530 A133531 A133532

Keyword

nonn

Author

Artur Jasinski, Sep 14 2007

Extensions

a(38)-a(41) from K. D. Bajpai, Jun 18 2015

Status

approved