|
%I #10 Jul 22 2022 16:20:11
%S 1,513,213796
%N Numbers n such that both prime(n)+n and prime(n)-n give a triangular number.
%C Intersection of A115882 and A115883.
%C The corresponding primes are 2, 3673, 2955107.
%C No more terms up to 10^12. - _Giovanni Resta_, Jan 26 2014
%e prime(1) is 2, and both 2+1=3 and 2-1=1 are triangular.
%t Select[Range[214000],AllTrue[{Sqrt[8(Prime[#]-#)+1],Sqrt[8(Prime[#]+#)+ 1]},OddQ]&] (* _Harvey P. Dale_, Jul 22 2022 *)
%o (PARI) lista(nn) = {p = primes(nn); for (n=1, #p, pn = p[n]; if (ispolygonal(pn - n, 3) && ispolygonal(pn + n, 3), print1(n, ", ")););}
%Y Cf. A115882, A115883.
%K nonn,bref,more
%O 1,2
%A _Michel Marcus_, Jan 25 2014
|
