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A034961
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Sums of three consecutive primes.
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51
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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
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1,1
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COMMENTS
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For prime terms see A034962. - Zak Seidov, Feb 17 2011
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LINKS
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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. A puzzle about these numbers.
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FORMULA
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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
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EXAMPLE
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a(1) = 10 = 2 + 3 + 5.
a(42) = 565 = 181 + 191 + 193.
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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Cf. A001043, A011974, A034707, A034962, A034963.
Sequence in context: A267329 A120138 A050200 * A207637 A171444 A227371
Adjacent sequences: A034958 A034959 A034960 * A034962 A034963 A034964
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KEYWORD
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nonn,easy
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AUTHOR
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Patrick De Geest, Oct 15 1998
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STATUS
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approved
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