A034961 Sums of three consecutive primes.

10, 15, 23, 31, 41, 49, 59, 71, 83, 97, 109, 121, 131, 143, 159, 173, 187, 199, 211, 223, 235, 251, 269, 287, 301, 311, 319, 329, 349, 371, 395, 407, 425, 439, 457, 471, 487, 503, 519, 533, 551, 565, 581, 589, 607, 633, 661, 679, 689, 701, 713, 731, 749, 771

Offset: 1

Author

Patrick De Geest, Oct 15 1998

Keywords

• nonn
• easy

Comments

For prime terms see A034962. - Zak Seidov, Feb 17 2011

Examples

			a(1) = 10 = 2 + 3 + 5.
a(42) = 565 = 181 + 191 + 193.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..1000
• Carlos Rivera, Puzzle 1021. p(k)+p(k+1)+1, The Prime Puzzles and Problems Connection.

Crossrefs

Cf. A001043, A011974, A034707, A034962, A034963.

Programs

Magma

[&+[ NthPrime(n+k): k in [0..2] ]: n in [1..50] ]; // Vincenzo Librandi, Apr 03 2011

Mathematica

Plus @@@ Partition[ Prime[ Range[60]], 3, 1] (* Robert G. Wilson v, Feb 11 2005 *)
3 MovingAverage[Prime[Range[60]], {1, 1, 1}] (* Jean-François Alcover, Nov 12 2018 *)

PARI

a(n)=my(p=prime(n),q=nextprime(p+1)); p+q+nextprime(q+1) \\ Charles R Greathouse IV, Jul 01 2013

PARI

is(n)=my(p=precprime(n\3),q=nextprime(n\3+1),r=n-p-q); if(r>q, r==nextprime(q+2), r==precprime(p-1) && r) \\ Charles R Greathouse IV, Jul 05 2017

Python

from sympy import nextprime
from itertools import count, islice
def agen(): # generator of terms
    p, q, r = 2, 3, 5
    while True:
        yield p + q + r
        p, q, r = q, r, nextprime(r)
print(list(islice(agen(), 54))) # Michael S. Branicky, Dec 27 2022

Sage

BB = primes_first_n(57)
L = []
for i in range(55):
    L.append(BB[i]+BB[i+1]+BB[i+2])
L # Zerinvary Lajos, May 14 2007

Formula

a(n) = Sum_{k=0..2} A000040(n+k). - Omar E. Pol, Feb 28 2020

a(n) = A001043(n) + A000040(n+2). - R. J. Mathar, May 25 2020