OFFSET
1,1
COMMENTS
Conjecture: (i) a(n) exists for any n > 0.
(ii) For each integer n > 2, there is a positive integer k with k*n - prime(k) prime.
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..50
Zhi-Wei Sun, A new theorem on the prime-counting function, arXiv:1409.5685 [math.NT], 2014-2017.
EXAMPLE
a(1) = 3 since prime(3) - 3*1 = 5 - 3 = 2 is prime.
MATHEMATICA
Do[k=1; Label[aa]; If[Prime[k]>k*n&&PrimeQ[Prime[k]-k*n], Print[n, " ", k]; Goto[bb]]; k=k+1; Goto[aa]; Label[bb]; Continue, {n, 1, 22}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Sep 28 2014
EXTENSIONS
Terms a(23) and beyond from Giovanni Resta, Apr 22 2020
STATUS
approved