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A309120 a(n) is the least k > 1 such that n*k is adjacent to a prime. 2


%S 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,

%T 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,

%U 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

%N a(n) is the least k > 1 such that n*k is adjacent to a prime.

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

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

%H Robert Israel, <a href="/A309120/b309120.txt">Table of n, a(n) for n = 1..10000</a>

%F a(A104278(n)) > 2 and a(A147820(n)) = 2. - _Ivan N. Ianakiev_, Jul 18 2019

%e 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.

%p f:= proc(m) local k;

%p for k from 2 by 1+(m mod 2) do

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

%p od

%p end proc:

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

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

%t a/@Range[94] (* _Ivan N. Ianakiev_, Jul 18 2019 *)

%o (PARI) a(n) = my(k=2); while (!isprime(n*k+1) && !isprime(n*k-1), k++); k; \\ _Michel Marcus_, Jul 19 2019

%Y Cf. A307833, A104278, A147820.

%K nonn

%O 1,1

%A _Robert Israel_, Jul 17 2019

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Last modified June 2 17:02 EDT 2020. Contains 334787 sequences. (Running on oeis4.)