cp's OEIS Frontend

A055469 Primes of the form k(k+1)/2+1 (i.e., central polygonal numbers, or one more than triangular numbers).

%I A055469 #32 May 14 2022 12:03:25
%S A055469 2,7,11,29,37,67,79,137,191,211,277,379,631,821,947,991,1129,1327,
%T A055469 1597,1831,2017,2081,2347,2557,2851,2927,3571,3917,4561,4657,4951,
%U A055469 5051,5779,6217,6329,8647,8779,9181,9871,11027,12721,13367,14029,14197,14879
%N A055469 Primes of the form k(k+1)/2+1 (i.e., central polygonal numbers, or one more than triangular numbers).
%C A055469 Also primes of the form (n^2 + 7)/8. - _Ray Chandler_, Oct 08 2005
%C A055469 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
%C A055469 n such that A000010(n) = A000217(k). - _Giovanni Teofilatto_, Jan 29 2010
%C A055469 It is conjectured that this sequence is infinite. - _Daniel Forgues_, Apr 21 2015
%H A055469 Vincenzo Librandi, <a href="/A055469/b055469.txt">Table of n, a(n) for n = 1..1000</a>
%F A055469 a(n) = A000124(A067186(n)) = (A110873(n) + 7)/8. - _Ray Chandler_, Oct 08 2005
%t A055469 Select[Table[(n^2 + 7)/8, {n, 400}], PrimeQ] (* _Ray Chandler_, Oct 08 2005 *)
%t A055469 Select[Accumulate[Range[400]]+1,PrimeQ] (* _Harvey P. Dale_, May 14 2022 *)
%o A055469 (PARI) forprime(p=2,10^5, if ( issquare(8*p-7), print1(p, ", "))) \\ _Joerg Arndt_, Jul 14 2012
%o A055469 (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
%Y A055469 Cf. A000040, A000124, A000217, A067186, A110872, A110873, A129545.
%K A055469 nonn,easy
%O A055469 1,1
%A A055469 _Henry Bottomley_, Jun 27 2000