A247895 - OEIS

%I #22 Apr 22 2020 06:54:44

%S 3,7,13,31,69,190,444,1052,2702,6455,15928,40073,100370,251707,637321,

%T 1617175,4124448,10553415,27066978,69709680,179992909,465769803,

%U 1208198532,3140421716,8179002120,21338685408,55762149030,145935689361,382465573486,1003652347100

%N Least integer k > 0 such that prime(k) - k*n is prime.

%C Conjecture: (i) a(n) exists for any n > 0.

%C (ii) For each integer n > 2, there is a positive integer k with k*n - prime(k) prime.

%H Giovanni Resta, <a href="/A247895/b247895.txt">Table of n, a(n) for n = 1..50</a>

%H Zhi-Wei Sun, <a href="http://arxiv.org/abs/1409.5685">A new theorem on the prime-counting function</a>, arXiv:1409.5685 [math.NT], 2014-2017.

%e a(1) = 3 since prime(3) - 3*1 = 5 - 3 = 2 is prime.

%t 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}]

%Y Cf. A000040, A247278, A247793.

%K nonn

%O 1,1

%A _Zhi-Wei Sun_, Sep 28 2014

%E Terms a(23) and beyond from _Giovanni Resta_, Apr 22 2020