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A034961 Sums of three consecutive primes. 53
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
For prime terms see A034962. - Zak Seidov, Feb 17 2011
LINKS
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
Sequence in context: A267329 A120138 A050200 * A207637 A171444 A227371
KEYWORD
nonn,easy
AUTHOR
Patrick De Geest, Oct 15 1998
STATUS
approved

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Last modified April 13 19:06 EDT 2024. Contains 371644 sequences. (Running on oeis4.)