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

Author

Artur Jasinski, Sep 14 2007

Keywords

• nonn

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

Examples

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

Links

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

Crossrefs

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

Programs

Magma

[&+[ NthPrime(n+i)^2 :  i in [0..2]] : n in [1..20]]; // K. D. Bajpai, Jun 17 2015

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 *)

PARI

for( n= 1, 100,  k= sum(i=n, n+2, prime(i)^2) ; print1(k, ", ")) \\ K. D. Bajpai, Jun 17 2015

Formula

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

Extensions

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