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A035096
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a(n) = smallest number k such that p(n)*k+1 is prime, where p(n) is the n-th prime.
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5
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1, 2, 2, 4, 2, 4, 6, 10, 2, 2, 10, 4, 2, 4, 6, 2, 12, 6, 4, 8, 4, 4, 2, 2, 4, 6, 6, 6, 10, 2, 4, 2, 6, 4, 8, 6, 10, 4, 14, 2, 2, 6, 2, 4, 18, 4, 10, 12, 24, 12, 2, 2, 6, 2, 6, 6, 8, 6, 4, 2, 6, 2, 4, 6, 6, 26, 6, 10, 6, 10, 14, 2, 6, 4, 12, 12, 24, 6, 8, 4, 2, 10, 2, 4, 10, 2, 8, 30
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| These arithmetic progressions have prime differences. Note that both the terms of generated by this k values and the differences are primes as well.
This is one possible generalization of "the least prime problem in special arithmetic progressions" when n in the nk+1 form is replaced by n-th prime number.
Comment from Max Alekseyev, Jul 11 2008: Note that Dirichlet's theorem on primes in arithmetic progressions implies that a(n) always exists.
If a(n)=2, p(n) is Sophie Germain prime (A005384). - Moshe Levin, Jan 28 2012
Among the first 10^6 terms, the largest is a(330408) = 234. - Moshe Levin, Jan 28 2012
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..10000
Eric Weisstein's World of Math, Dirichlet's theorem
Index entries for sequences related to primes in arithmetic progressions
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EXAMPLE
| a(15)=6 because the 15th prime is 47, and the smallest k such that 47k+1 is prime is k=6, for which 47k+1=283.
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MATHEMATICA
| Reap[Sow[1]; Do[p = Prime[n]; k = 2; While[! PrimeQ[k*p + 1], k = k + 2];
Sow[k], {n, 2, 10^4}]][[2, 1]] (* Moshe Levin, Jan 28 2012 *)
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CROSSREFS
| Smallest k such that k*n+1 is prime is A034693. Sophie Germain primes are in A005384.
Sequence in context: A106264 A152423 A170905 * A066675 A097800 A183402
Adjacent sequences: A035093 A035094 A035095 * A035097 A035098 A035099
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu)
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