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A294078
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a(n) is the smallest even number k such that k*prime(n) - 1 or k*prime(n) + 1 is prime.
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0
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2, 2, 2, 2, 2, 4, 4, 2, 2, 2, 2, 2, 2, 4, 6, 2, 6, 6, 4, 4, 4, 2, 2, 2, 2, 6, 6, 6, 6, 2, 4, 2, 4, 2, 8, 6, 2, 4, 10, 2, 2, 6, 2, 4, 4, 2, 2, 8, 4, 2, 2, 2, 6, 2, 6, 4, 6, 2, 4, 2, 6, 2, 2, 6, 6, 6, 2, 2, 6, 8, 10, 2, 2, 4, 2, 4, 6, 6, 8, 4
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OFFSET
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1,1
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COMMENTS
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For n <= 10^9 the largest term is 186.
First occurrence of 2k, k=1,2,3,...: 1, 6, 15, 35, 39, 117, 1134, 199, 152, 362, ..., . - Robert G. Wilson v, Feb 08 2018
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LINKS
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EXAMPLE
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For n = 6, prime(6) = 13. The smallest even number k such that k * 13 + 1 is a prime number is k = 4, because 4 * 13 + 1 = 53 (not k = 2). So 4 is the sixth term.
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MATHEMATICA
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f[n_] := Block[{k = 2, p = Prime@ n}, While[ !PrimeQ[k*p -1] && !PrimeQ[k*p +1], k += 2]; k]; Array[f, 100] (* Robert G. Wilson v, Feb 08 2018 *)
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PROG
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(PARI) {
forprime(p=2, 100,
k=2;
while(!isprime(k*p-1)&&!isprime(k*p+1), k+=2);
print1(k", ");
)
}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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