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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. 4
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 (list; graph; refs; listen; history; text; internal format)
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: A100765 A092168 A352605 * A289270 A262555 A343814

Adjacent sequences:  A229077 A229078 A229079 * A229081 A229082 A229083

KEYWORD

nonn

AUTHOR

K. D. Bajpai, Sep 12 2013

STATUS

approved

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Last modified October 6 04:31 EDT 2022. Contains 357261 sequences. (Running on oeis4.)