cp's OEIS Frontend

A229080 Primes of the form T(k) + S(k) + 1 where T(k) is the k-th triangular number and S(k) is the k-th square number.

%I A229080 #15 Jul 14 2021 08:38:14
%S A229080 3,41,101,127,223,443,673,877,1277,1553,2543,2927,3061,4241,4733,4903,
%T A229080 5431,6971,7177,8933,9883,10627,11927,12743,13873,17551,19211,20593,
%U A229080 21661,26203,31177,33377,36583,40427,51431,58313,60101,60703,67523,68161,75377,81551
%N A229080 Primes of the form T(k) + S(k) + 1 where T(k) is the k-th triangular number and S(k) is the k-th square number.
%C A229080 Also primes of the form (3k^2 + k + 2)/2.
%H A229080 K. D. Bajpai, <a href="/A229080/b229080.txt">Table of n, a(n) for n = 1..10000</a>
%e A229080 T(8) + S(8) + 1 = 8*(8+1)/2 + 8^2 + 1 = 101, which is prime, so 101 is a term.
%e A229080 T(9) + S(9) + 1 = 9*(9+1)/2 + 9^2 + 1 = 127, which is prime, so 127 is a term.
%p A229080 KD:= proc() local a,b,d;  a:= (1/2)*x*(x+1); b:=x^2; d:=a+b+1;  if isprime(d) then   RETURN(d): fi; end: seq(KD(),x=1..500);
%Y A229080 Cf. A000217, A000290, A120479.
%K A229080 nonn
%O A229080 1,1
%A A229080 _K. D. Bajpai_, Sep 12 2013