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A120223 a(n) is the minimal number k>1 such that n+k and n*k+1 are primes. 6
2, 3, 2, 3, 2, 5, 4, 5, 2, 3, 2, 5, 4, 3, 2, 7, 6, 11, 10, 3, 2, 9, 6, 13, 4, 3, 4, 15, 2, 7, 10, 11, 10, 3, 2, 5, 4, 5, 2, 7, 2, 5, 4, 9, 14, 13, 6, 5, 4, 3, 2, 21, 14, 5, 6, 5, 4, 9, 12, 7, 6, 5, 10, 3, 2, 5, 4, 15, 2, 3, 8, 25, 6, 27, 8, 3, 6, 11, 4, 3, 2, 15, 6, 5, 12, 11, 20, 15, 12, 7, 6, 5, 4, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

If n+1 is prime then a(n)>A085063(n); if n+1 is not prime then a(n)=A085063(n).

LINKS

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

EXAMPLE

a(3)=2 because 3+2=5 and 3*2+1=7 are prime;

a(8)=5 because 8+5=13 and 8*5+1=41 are prime.

MAPLE

f:= proc(n) local k;

  for k from `if`( n::odd, 2, 3) do

     if isprime(n*k+1) and isprime(n+k) then return k fi

  od

end proc:

map(f, [$1..100]); # Robert Israel, Feb 03 2019

MATHEMATICA

Reap[Do[Do[If[PrimeQ[{n+x, n*x+1}]=={True, True}, Sow[x]; Break[]], {x, 2, 100}], {n, 120}]][[2, 1]]

mnk[n_]:=Module[{k=2}, While[!AllTrue[{n+k, n*k+1}, PrimeQ], k++]; k]; Array[ mnk, 100] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Oct 15 2014 *)

PROG

(PARI) for(n=1, 100, k=2; while(!isprime(n+k), k++; while(!isprime(n*k+1), k++)); print1(k, ", ")) \\ Jinyuan Wang, Feb 04 2019

CROSSREFS

Cf. A085063, A092945, A085063, A120224, A120225.

Sequence in context: A204895 A064652 A077600 * A282691 A346744 A265577

Adjacent sequences:  A120220 A120221 A120222 * A120224 A120225 A120226

KEYWORD

nonn

AUTHOR

Zak Seidov, Jun 10 2006

STATUS

approved

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Last modified May 27 16:48 EDT 2022. Contains 354110 sequences. (Running on oeis4.)