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Search: id:A108317
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| A108317 |
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Smallest a(n) such that a(n) n's plus a(n) is prime, or 0 if no such a(n) exists. |
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1
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| 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
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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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 (njas(AT)research.att.com).
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.
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FORMULA
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a(A016789(n)) = a(A017509(n)) = 0 for n >= 1. a(n) = 1 iff n is a term of A006093. - Rick L. Shepherd (rshepherd2(AT)hotmail.com), Jul 26 2005
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EXAMPLE
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a(13)=4: 4 13s plus 4 = 13131313+4 = 13131317, which is prime.
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MATHEMATICA
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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 *) (from Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 30 2005)
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PROGRAM
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(PARI) /* for nonzero terms */ a(n) = m=1; pr=n; while(!isprime(pr+m), m++; pr=eval(concat(Str(pr), n))); m (Shepherd)
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CROSSREFS
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Cf. A006093 (primes minus 1), A016789 (3n + 2), A017509 (11n + 10).
Sequence in context: A001163 A140791 A158527 this_sequence A114825 A131492 A090945
Adjacent sequences: A108314 A108315 A108316 this_sequence A108318 A108319 A108320
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KEYWORD
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base,nonn
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AUTHOR
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Ray G. Opao (1260(AT)email.com), Jun 30 2005
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EXTENSIONS
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a(33) - a(78) from Robert G. Wilson v (rgwv(at)rgwv.com) with guidance from Rick L. Shepherd (rshepherd2(AT)hotmail.com), 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 (rgwv(at)rgwv.com), Jul 28 2005
a(79)>14179 - Robert G. Wilson v (rgwv(at)rgwv.com), Jul 28 2005
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