%I #18 Mar 21 2015 01:52:49
%S 1,1,140,1,0,1,2,0,2,1,0,1,4,0,4,1,0,1,4,0,0,1,0,23,4,0,2,1,0,1,8,0,
%T 4198,497,0,1,2,0,8,1,0,1,0,0,2,1,0,35,2,0,2,1,0,0,2,0,4,1,0,1,2,0,4,
%U 17,0,1,64,0,2,1,0,1,14,0,2,0,0,1
%N Smallest a(n) such that a(n) n's plus a(n) is prime, or 0 if no such a(n) exists.
%C Some of the larger entries may only correspond to probable primes.
%C Some or all of the zero values are merely conjectures. - _N. J. A. Sloane_
%C a(n)=0 for n = 3m+2 (1<=m) (they are all divisible by 3) or n=11m+10 (1<=m<9) (they are all divisible by 11) and if a(n) is not 0 then n and a(n) are of opposite parity. - _Robert G. Wilson v_ and _Rick L. Shepherd_, Jul 28 2005
%C The sequence continues: 0,4490,1,0,13,14,0,0,1,0,349,10,0,86,2539,0,1,4,0,124,1,0,1,4,0,2,1,0,1,2,0,302,1,0,83,2,0,2,5,0,a(120)>5364,2,0,278,5,0,...,. - _Robert G. Wilson v_, Jul 28 2005
%C a(79)>14179. - _Robert G. Wilson v_, Jul 28 2005
%F a(A016789(n)) = a(A017509(n)) = 0 for n >= 1. a(n) = 1 iff n is a term of A006093. - _Rick L. Shepherd_, Jul 26 2005
%e a(13)=4: 4 13s plus 4 = 13131313+4 = 13131317, which is prime.
%t f[n_] := If[(n > 4 && Mod[n, 3] == 2) || (n > 20 && Mod[n, 11] == 10), k = 0, If[n == 1, k = 1, Block[{id = IntegerDigits[n]}, k = Mod[n, 2] + 1; While[ !PrimeQ[ FromDigits[ Flatten[ Table[id, {k}]]] + k], k += 2]]]; k]; Table[ f[n], {n, 100}] (* only good for n<109 *) (* _Robert G. Wilson v_, Jun 30 2005 *)
%o (PARI) /* for nonzero terms */ a(n) = m=1;pr=n;while(!isprime(pr+m),m++;pr=eval(concat(Str(pr),n)));m \\ _Rick L. Shepherd_, Jul 26 2005
%Y Cf. A006093 (primes minus 1), A016789 (3n + 2), A017509 (11n + 10).
%K base,nonn
%O 1,3
%A _Ray G. Opao_, Jun 30 2005
%E a(33) - a(78) from _Robert G. Wilson v_ with guidance from _Rick L. Shepherd_, Jul 28 2005