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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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20
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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
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OFFSET
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1,1
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COMMENTS
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Also primes of the form (n^2 + 7)/8. - Ray Chandler, 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, Apr 05 2002
It is conjectured that this sequence is infinite. - Daniel Forgues, Apr 21 2015
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LINKS
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FORMULA
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MATHEMATICA
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Select[Table[(n^2 + 7)/8, {n, 400}], PrimeQ] (* Ray Chandler, Oct 08 2005 *)
Select[Accumulate[Range[400]]+1, PrimeQ] (* Harvey P. Dale, May 14 2022 *)
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PROG
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(PARI) forprime(p=2, 10^5, if ( issquare(8*p-7), print1(p, ", "))) \\ Joerg Arndt, Jul 14 2012
(PARI) list(lim)=my(v=List(), p); forstep(s=3, sqrtint(lim\1*8-7), 2, if(isprime(p=(s^2+7)/8), listput(v, p))); Vec(v) \\ Charles R Greathouse IV, May 05 2020
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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