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A055469
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Primes of the form k(k+1)/2+1 (i.e. central polygonal numbers, or one more than triangular numbers).
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11
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2, 7, 11, 29, 37, 67, 79, 137, 191, 211, 277, 379, 631, 821, 947, 991, 1129, 1327, 1597, 1831, 2017, 2081, 2347, 2557, 2851, 2927, 3571, 3917, 4561, 4657, 4951, 5051, 5779, 6217, 6329, 8647, 8779, 9181, 9871, 11027, 12721, 13367, 14029, 14197, 14879
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Also primes of the form (n^2+7)/8. - Ray Chandler (rayjchandler(AT)sbcglobal.net), Oct 08 2005
q=2 and q=5 are the only primes values such that q+1 is a triangular number because 8q+9 is a square for 2 and 5 only. - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 05 2002
n such that A000010(n) = A000217(k) [From Giovanni Teofilatto (g.teofilatto(AT)tiscalinet.it), Jan 29 2010]
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FORMULA
| a(n) = A000124(A067186(n)) = (A110873(n) + 7)/8. - Chandler
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MATHEMATICA
| Select[Table[(n^2 + 7)/8, {n, 400}], PrimeQ] (*Chandler*)
s=0; lst={}; Do[s+=n; p=s+1; If[PrimeQ[p], AppendTo[lst, p]], {n, 0, 6!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Apr 03 2009]
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PROG
| (PARI) for(n=1, 4000, if(sqrt(8*prime(n)-7)==floor(sqrt(8*prime(n)-7), print1(prime(n), ", ")))
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CROSSREFS
| Cf. A000040, A000124, A000217, A067186, A110872, A110873.
Sequence in context: A024591 A073602 A057025 * A123151 A026133 A026162
Adjacent sequences: A055466 A055467 A055468 * A055470 A055471 A055472
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KEYWORD
| nonn
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Jun 27 2000
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