A307833 Smallest k > 1 such that A014574(n)*k is adjacent to a prime.
2, 2, 2, 2, 2, 2, 3, 5, 3, 4, 2, 3, 2, 2, 2, 2, 2, 2, 2, 3, 5, 2, 2, 4, 3, 3, 2, 2, 2, 2, 2, 3, 2, 4, 3, 2, 2, 2, 3, 6, 3, 2, 2, 2, 3, 4, 2, 2, 2, 3, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 4, 2, 3, 2, 3, 2, 2, 4, 3, 2, 2, 5, 2, 4, 4, 4, 4, 3, 2, 5, 2, 3, 4, 2, 4, 4, 2, 2, 2, 4, 2, 6, 4, 2, 2, 5, 4, 6
Offset: 1
Keywords
Examples
72*5 = 360, which is adjacent to the prime 359, so a(8) = 5.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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Maple
P:= {seq(ithprime(i),i=1..10^4)}: A014574:= sort(convert(map(t -> t+1, P intersect map(`-`,P,2)),list)): f:= proc(m) local k; for k from 2 do if isprime(k*m-1) or isprime(k*m+1) then return k fi od end proc: map(f, A014574); # Robert Israel, Jul 17 2019 -
Mathematica
primeNearQ[n_] := AnyTrue[{-1, 1} + n, PrimeQ]; twinMidQ[n_] := AllTrue[{-1, 1} + n, PrimeQ]; f[n_] := Module[{k = 2}, While[! primeNearQ[k*n], k++]; k]; f /@ Select[Range[10^4], twinMidQ] (* Amiram Eldar, Jul 05 2019 *) -
PARI
isok2(n) = isprime(n-1) && isprime(n+1); k(n) = my(k=2); while (! (isprime(n*k-1) || isprime(n*k+1)), k++); k; lista(nn) = for (n=1, nn, if (isok2(n), print1(k(n), ", "))); \\ Michel Marcus, May 01 2019
Comments