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.

3, 41, 101, 127, 223, 443, 673, 877, 1277, 1553, 2543, 2927, 3061, 4241, 4733, 4903, 5431, 6971, 7177, 8933, 9883, 10627, 11927, 12743, 13873, 17551, 19211, 20593, 21661, 26203, 31177, 33377, 36583, 40427, 51431, 58313, 60101, 60703, 67523, 68161, 75377, 81551

Offset: 1

Author

K. D. Bajpai, Sep 12 2013

Keywords

• nonn

Comments

Also primes of the form (3k^2 + k + 2)/2.

Examples

			T(8) + S(8) + 1 = 8*(8+1)/2 + 8^2 + 1 = 101, which is prime, so 101 is a term.
T(9) + S(9) + 1 = 9*(9+1)/2 + 9^2 + 1 = 127, which is prime, so 127 is a term.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000217, A000290, A120479.

Programs

Maple

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);