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

1,1

Comments

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

Links

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

Example

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.

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);

Crossrefs

Cf. A000217, A000290, A120479.

Sequence in context: A092168 A352605 A360930 * A289270 A262555 A343814

Adjacent sequences: A229077 A229078 A229079 * A229081 A229082 A229083

Keyword

nonn

Author

K. D. Bajpai, Sep 12 2013

Status

approved