cp's OEIS Frontend

A219432 Least 3-smooth number k such that prime(n)*k - 1 is prime.

%I A219432 #28 Nov 23 2012 19:34:28
%S A219432 2,1,4,2,4,8,4,2,6,6,2,2,4,6,6,4,6,8,6,4,108,2,4,16,2,24,6,6,6,6,6,4,
%T A219432 4,2,12,12,2,6,12,4,18,8,24,8,4,2,2,8,4,2,16,6,18,12,12,4,6,2,12,4,6,
%U A219432 4,2,72,6,6,2,2,6,8,16,6,2,6,2,4,6,6,24,8,16,12
%N A219432 Least 3-smooth number k such that prime(n)*k - 1 is prime.
%C A219432 Conjecture: a(n) < prime(n) for n > 21. Conjecture confirmed up to a(122578) = 55296 < prime(122578) = 1620539.
%H A219432 Lei Zhou, <a href="/A219432/b219432.txt">Table of n, a(n) for n = 1..10000</a>
%e A219432 prime(1) = 2, 2 * 2 - 1 = 3 is prime, so a(1)=2;
%e A219432 prime(2) = 3, 3 * 1 - 1 = 2 is prime, so a(2)=1;
%e A219432 ......
%e A219432 prime(6) = 13, 13 * 2 - 1 = 25 is not prime,
%e A219432            13 * 3 - 1 = 38 is not prime,
%e A219432            13 * 4 - 1 = 51 is not prime,
%e A219432            13 * 6 - 1 = 77 is not prime,
%e A219432            13 * 8 - 1 = 103 is prime, so a(6)=8.
%t A219432 f[n_] := Block[{p2, p3 = 3^Range[0, Floor@ Log[3, n] + 1]}, p2 = 2^Floor[Log[2, n/p3] + 1]; Min[ Select[ p2*p3, IntegerQ]]]; Table[pr=Prime[i]; j=1; fj=0; While[j++; fj=f[fj+0.5]; cp=-1+pr*fj; !PrimeQ[cp]]; fj, {i, 116}]
%Y A219432 Cf. A003586, A216568.
%K A219432 nonn
%O A219432 1,1
%A A219432 _Lei Zhou_, Nov 19 2012