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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 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: A267329 A120138 A050200 * A207637 A171444 A227371 Adjacent sequences: A034958 A034959 A034960 * A034962 A034963 A034964 KEYWORD nonn,easy AUTHOR Patrick De Geest, Oct 15 1998 STATUS approved

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Last modified September 22 18:10 EDT 2023. Contains 365531 sequences. (Running on oeis4.)