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A241886
a(n) = smallest prime p such that there is a gap of n*(n+1) between p and the next prime.
1
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
Sequence in context: A093155 A370105 A372506 * A096649 A370283 A235131
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