

A108317


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


0



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
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OFFSET

1,3


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


LINKS

Table of n, a(n) for n=1..78.


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


EXAMPLE

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


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 *)


PROG

(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


CROSSREFS

Cf. A006093 (primes minus 1), A016789 (3n + 2), A017509 (11n + 10).
Sequence in context: A188452 A183491 A215571 * A252963 A114825 A308617
Adjacent sequences: A108314 A108315 A108316 * A108318 A108319 A108320


KEYWORD

base,nonn


AUTHOR

Ray G. Opao, Jun 30 2005


EXTENSIONS

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


STATUS

approved



