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A294078 a(n) is the smallest even number k such that k*prime(n) - 1 or k*prime(n) + 1 is prime. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

Table of n, a(n) for n=1..80.

EXAMPLE

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.

MATHEMATICA

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 *)

PROG

(PARI) {

  forprime(p=2, 100,

    k=2;

    while(!isprime(k*p-1)&&!isprime(k*p+1), k+=2);

    print1(k", ");

  )

}

CROSSREFS

Cf. A000040, A071407 (with "and" rather than "or").

Sequence in context: A319819 A319820 A319799 * A064133 A295101 A160675

Adjacent sequences:  A294075 A294076 A294077 * A294079 A294080 A294081

KEYWORD

nonn

AUTHOR

Dimitris Valianatos, Feb 07 2018

STATUS

approved

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Last modified July 26 08:42 EDT 2021. Contains 346294 sequences. (Running on oeis4.)