A241886 a(n) = smallest prime p such that there is a gap of n*(n+1) between p and the next prime.

3, 23, 199, 887, 4297, 16141, 82073, 31397, 404851, 1468277, 1357201, 17983717, 36271601, 20831323, 391995431, 1851255191, 3917587237, 12010745569, 23323808741, 82490815123, 400729567081, 1339347750707, 2210401546601, 4872634110067, 5120731250207

Offset

1,1

Links

Jens Kruse Andersen, Table of n, a(n) for n = 1..36

Thomas R. Nicely, First occurrence prime gaps [For local copy see A000101]

Formula

a(n) = A000230(n*(n+1)/2). - Jens Kruse Andersen, Oct 01 2014

Example

a(3) = 199 because 199 and 211 are consecutive primes with difference 3*4=12.

Prog

(Python)
import sympy
n = 1
while n >= 0 and n <= 10:
    p = 2
    while sympy.nextprime(p) - p != (n * (n + 1)):
        p = sympy.nextprime(p)
    print(p, end=", ")
    n = n + 1
    p = sympy.nextprime(p)

Crossrefs

Cf. A000230, A001223.

Sequence in context: A093155 A370105 A372506 * A096649 A370283 A235131

Adjacent sequences: A241883 A241884 A241885 * A241887 A241888 A241889

Keyword

nonn,hard

Author

Abhiram R Devesh, Aug 09 2014

Extensions

Definition corrected and more terms using Nicely link from Jens Kruse Andersen, Oct 01 2014

Status

approved