A114951 Numbers k such that the sum of the k-th triangular number and the k-th prime is prime.

1, 3, 4, 11, 15, 19, 20, 23, 24, 32, 39, 48, 51, 60, 67, 68, 71, 75, 83, 84, 88, 95, 100, 104, 111, 119, 120, 127, 132, 135, 143, 147, 168, 180, 183, 191, 195, 200, 203, 204, 207, 211, 212, 219, 236, 240, 243, 251, 252, 255, 275, 276, 284

Offset

1,2

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

The 11th triangular number is 66, the 11th prime is 31.
Their sum is 97, a prime. Therefore 11 is in the sequence.

Mathematica

Select[Range[500], PrimeQ[ #*(# + 1)/2 + Prime[ # ]] &]

Prog

(PARI) list(lim)=my(v=List(), n); forprime(p=2, , if(n++>lim, break); if(isprime(n*(n+1)/2+p), listput(v, n))); Vec(v) \\ Charles R Greathouse IV, Jun 13 2017

Crossrefs

Cf. A000217.

Sequence in context: A295067 A263262 A249650 * A085368 A041405 A042483

Adjacent sequences: A114948 A114949 A114950 * A114952 A114953 A114954

Keyword

nonn,less

Author

J. M. Bergot, Jun 23 2007

Extensions

Edited and extended by Stefan Steinerberger and Robert G. Wilson v, Jun 24 2007

Status

approved