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A309120 a(n) is the least k > 1 such that n*k is adjacent to a prime. 2
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 4, 2, 2, 3, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 6, 3, 6, 5, 2, 2, 2, 2, 4, 2, 2, 2, 4, 5, 4, 2, 2, 2, 4, 2, 2, 3, 2, 2, 2, 2, 6, 2, 2, 3, 2, 2, 2, 3, 4, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

If n is odd then a(n) is even.

a(n) exists by Dirichlet's theorem on primes in arithmetic progressions.

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

a(A104278(n)) > 2 and a(A147820(n)) = 2. - Ivan N. Ianakiev, Jul 18 2019

EXAMPLE

a(13)=4 because 4*13+1=53 is prime but none of 2*13-1,2*13+1,3*13-1,3*13+1 are primes.

MAPLE

f:= proc(m) local k;

  for k from 2 by 1+(m mod 2) do

    if isprime(k*m-1) or isprime(k*m+1) then return k fi

  od

end proc:

map(f, [$1..100]);

MATHEMATICA

a[n_]:=Module[{k=2}, While[Not[PrimeQ[k*n-1]||PrimeQ[k*n+1]], k++]; k];

a/@Range[94] (* Ivan N. Ianakiev, Jul 18 2019 *)

PROG

(PARI) a(n) = my(k=2); while (!isprime(n*k+1) && !isprime(n*k-1), k++); k; \\ Michel Marcus, Jul 19 2019

CROSSREFS

Cf. A307833, A104278, A147820.

Sequence in context: A094382 A146167 A103380 * A098708 A067394 A076925

Adjacent sequences:  A309117 A309118 A309119 * A309121 A309122 A309123

KEYWORD

nonn

AUTHOR

Robert Israel, Jul 17 2019

STATUS

approved

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Last modified April 6 21:24 EDT 2020. Contains 333286 sequences. (Running on oeis4.)