A229469 - OEIS

A229469

Numbers n such that T(n) + S(n) + 1 is prime, where T(n) and S(n) are the n-th triangular and square numbers.

1, 5, 8, 9, 12, 17, 21, 24, 29, 32, 41, 44, 45, 53, 56, 57, 60, 68, 69, 77, 81, 84, 89, 92, 96, 108, 113, 117, 120, 132, 144, 149, 156, 164, 185, 197, 200, 201, 212, 213, 224, 233, 236, 248, 252, 260, 264, 269, 281, 288, 300, 312, 317, 321, 324, 329, 344, 353

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

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

EXAMPLE

a(4)=9: T(9)+S(9)+1= 9/2*(9+1)+9^2+1= 127 which is prime.

a(5)=12: T(12)+S(12)+1= 12/2*(12+1)+12^2+1= 223 which is prime.

MAPLE

KD:= proc() local a, b, c, d; a:= n/2*(n+1)+n^2+1; if isprime(a) then RETURN(n): fi; end: seq(KD(), n=1..5000);

PROG

(PARI) v=List(); for(n=1, 10^5, if(isprime(n/2*(n+1)+n^2+1), listput(v, n))); Vec(v)