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%I #41 Mar 13 2018 12:53:17
%S 1,2,2,4,2,4,6,12,2,2,12,4,2,4,6,2,12,6,4,8,4,4,2,2,4,6,6,6,24,2,4,2,
%T 6,4,8,6,24,4,48,2,2,6,2,4,18,4,72,12,24,12,2,2,6,2,6,6,8,6,4,2,6,2,4,
%U 6,6,48,6,16,6,24,96,2,6,4,12,12,24,6,8,4,2,16
%N a(n) is the smallest 3-smooth number such that prime(n)*a(n) + 1 is prime.
%C Conjecture: a(n) < prime(n) except for a(522720).
%C a(522720)=12582912 > p(522720)=7728803.
%C Conjecture tested up to a(1000000).
%H Lei Zhou, <a href="/A219433/b219433.txt">Table of n, a(n) for n = 1..10000</a>
%e prime(1) = 2, 2 * 1 + 1 = 3 is prime, so a(1)=1;
%e prime(2) = 3, 3 * 2 + 1 = 7 is prime, so a(2)=2;
%e ......
%e prime(7) = 17, 17 * 1 + 1 = 18 is not prime,
%e 17 * 2 + 1 = 35 is not prime,
%e 17 * 3 + 1 = 52 is not prime,
%e 17 * 4 + 1 = 69 is not prime,
%e 17 * 6 + 1 = 103 is prime, so a(7)=6
%t 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+1/2]; cp=1+pr*fj; !PrimeQ[cp]]; fj, {i, 115}]
%Y Cf. A003586.
%K nonn,easy
%O 1,2
%A _Lei Zhou_, Nov 19 2012
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