A108317 Smallest a(n) such that a(n) n's plus a(n) is prime, or 0 if no such a(n) exists.

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, 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, 17, 0, 1, 64, 0, 2, 1, 0, 1, 14, 0, 2, 0, 0, 1

Offset: 1

Author

Ray G. Opao, Jun 30 2005

Keywords

• base
• nonn

Comments

Some of the larger entries may only correspond to probable primes.

Some or all of the zero values are merely conjectures. - N. J. A. Sloane

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

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

a(79)>14179. - Robert G. Wilson v, Jul 28 2005

Examples

			a(13)=4: 4 13s plus 4 = 13131313+4 = 13131317, which is prime.
		

Crossrefs

Cf. A006093 (primes minus 1), A016789 (3n + 2), A017509 (11n + 10).

Programs

Mathematica

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 *)

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

Formula

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

Extensions

a(33) - a(78) from Robert G. Wilson v with guidance from Rick L. Shepherd, Jul 28 2005