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

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)
(PARI) is(n)=isprime(n*(3*n+1)/2+1) \\ Charles R Greathouse IV, Sep 24 2013

Crossrefs

Cf. A228908, A229157.

Sequence in context: A066467 A180244 A072833 * A314574 A314575 A286454

Adjacent sequences: A229466 A229467 A229468 * A229470 A229471 A229472

Keyword

nonn,easy

Author

K. D. Bajpai, Sep 24 2013

Status

approved