OFFSET
2,3
COMMENTS
Conjecture: a(n) exists for any n > 1.
Note that k*n - prime(k) < 0 if k > e^(n + 1).
LINKS
Zhi-Wei Sun, Table of n, a(n) for n = 2..10000
Zhi-Wei Sun, A new theorem on the prime-counting function, arXiv:1409.5685, 2014.
Zhi-Wei Sun, A new theorem on the prime-counting function, Ramanujan J. 42 (2017), no.1, 59-67. (Cf. Conjecture 4.1.)
FORMULA
a(A059100(n)) = 1. - Michel Marcus, Sep 28 2014
EXAMPLE
a(5) = 29 since 29 * 5 - prime(29) = 145 - 109 = 6^2.
MATHEMATICA
SQ[n_] := IntegerQ[Sqrt[n]]
Do[k = 1; Label[aa]; If[SQ[k * n - Prime[k]], Print[n, " ", k]; Goto[bb]]; k = k + 1; Goto[aa]; Label[bb]; Continue, {n, 2, 60}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Sep 27 2014
STATUS
approved