OFFSET
1,1
COMMENTS
It is known that prime(k) <= k*(k+1) for any positive integer k. The conjecture in A235613 implies that the sequence has infinitely many terms.
Conjecture: This sequence contains infinitely many primes.
LINKS
Zhi-Wei Sun, Table of n, a(n) for n = 1..10000
EXAMPLE
a(1) = 2 since 1*2 - prime(1) = 0 is not prime, but 2*3 - prime(2) = 3 is prime.
a(2) = 3 since 3*4 - prime(3) = 7 is prime.
a(3) = 4 since 4*5 - prime(4) = 13 is prime.
MATHEMATICA
n=0; Do[If[PrimeQ[k(k+1)-Prime[k]], n=n+1; Print[n, " ", k]], {k, 1, 200}]
Select[Range[200], PrimeQ[(#(#+1))-Prime[#]]&] (* Harvey P. Dale, Apr 10 2020 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Jan 12 2014
STATUS
approved