A034961 - OEIS

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

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OFFSET

1,1

COMMENTS

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

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.

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

EXAMPLE

a(1) = 10 = 2 + 3 + 5.

a(42) = 565 = 181 + 191 + 193.

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 *)

PROG

(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

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

(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

CROSSREFS

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

Sequence in context: A120138 A373613 A050200 * A207637 A171444 A227371