A100500 a(n) = prime(3n-2) + prime(3n-1) + prime(3n).

10, 31, 59, 97, 131, 173, 211, 251, 301, 329, 395, 439, 487, 533, 581, 633, 689, 731, 789, 829, 883, 941, 1015, 1061, 1119, 1169, 1229, 1285, 1331, 1381, 1433, 1493, 1553, 1645, 1703, 1757, 1807, 1849, 1915, 1959, 2011, 2075, 2155, 2215, 2269, 2329, 2417, 2471

Offset: 1

Author

Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Nov 23 2004

Keywords

• nonn

Examples

			a(1) = 10 = 2 + 3 + 5 = prime(1) + prime(2) + prime(3).
a(2) = 31 = 7 + 11 + 13 = prime(4) + prime(5) + prime(6).
a(3) = 59 = 17 + 19 + 23 = prime(7) + prime(8) + prime(9).
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• C. Caldwell, List of small primes.

Crossrefs

Cf. A000040, A034961.

Programs

Magma

[&+[NthPrime(n+k): k in [0..2]]: n in [1..1000 by 3]]; // Vincenzo Librandi, Apr 23 2011

Mathematica

Total/@Partition[Prime[Range[150]],3] (* Harvey P. Dale, May 25 2011 *)

Python

from sympy import prime, nextprime
def a(n):
    p = prime(3*n - 2); q = nextprime(p); r = nextprime(q)
    return p + q + r
print([a(n) for n in range(1, 49)]) # Michael S. Branicky, Oct 31 2021

SageMath

def A100500(n): return sum(nth_prime(3*n-j) for j in range(3))
[A100500(n) for n in range(1,61)] # G. C. Greubel, Apr 03 2023

Formula

a(n) = A034961(3n-2). - R. J. Mathar, Apr 20 2009, Jun 17 2009