A103790 - OEIS

%I #3 Mar 31 2012 10:23:47

%S 0,1,1,3,1,3,1,5,3,1,3,3,1,5,3,3,1,3,3,1,3,5,3,9,3,1,3,1,7,9,5,3,1,5,

%T 1,3,3,5,3,3,1,5,1,3,1,7,7,3,1,5,3,1,5,3,3,3,1,3,3,1,5,9,3,1,13,7,3,5,

%U 1,5,3,7,3,3,5,3,7,11,7,5,1,5,1,3,5,3,7,3,1,15,11,7,13,7,5,3,9,1,13,3,5,3,3

%N a(n) = the minimum k that makes prime(n)+A019565(k) prime.

%C All elements except the first one are odd. This suggests a new way looking for large primes candidates.

%e Prime(1)+A019565(0)=2+1=3 is prime, so a(1)=0;

%e Prime(4)+A019565(3)=7+6=13 is prime, so a(4)=3;

%t A019565 = Function[tn, k1 = tn; o = 1; tt = 1; While[k1 > 0, k2 = Mod[k1, 2]; If[k2 == 1, tt = tt*Prime[o]]; k1 = (k1 - k2)/2; o = o + 1]; tt]; Do[npd = Prime[n]; ts = 1; tt = ts; cp = npd + A019565[tt]; While[ ! (PrimeQ[cp]), ts = ts + 1; tt = ts; cp = npd + A019565[ tt]]; Print[ts], {n, 3, 200} ]

%Y Cf. A019565.

%K easy,nonn

%O 1,4

%A _Lei Zhou_, Feb 16 2005