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A085063
a(n) is the minimal number k such that n+k and n*k+1 are primes.
7
1, 1, 2, 1, 2, 1, 4, 5, 2, 1, 2, 1, 4, 3, 2, 1, 6, 1, 10, 3, 2, 1, 6, 13, 4, 3, 4, 1, 2, 1, 10, 11, 10, 3, 2, 1, 4, 5, 2, 1, 2, 1, 4, 9, 14, 1, 6, 5, 4, 3, 2, 1, 14, 5, 6, 5, 4, 1, 12, 1, 6, 5, 10, 3, 2, 1, 4, 15, 2, 1, 8, 1, 6, 27, 8, 3, 6, 1, 4, 3, 2, 1, 6, 5, 12, 11, 20, 1, 12, 7, 6, 5, 4, 3, 2, 1, 4, 5
OFFSET
1,3
COMMENTS
If n+1 is prime then a(n)=1; if n+1 is not prime then a(n)=A120223(n).
LINKS
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 1+(n mod 2) by 2 do
if isprime(n+k) and isprime(n*k+1) then return k fi
od
end proc:
f(1):= 1: # Robert Israel, May 14 2018
MATHEMATICA
Reap[Do[Do[If[PrimeQ[{n+x, n*x+1}]=={True, True}, Sow[x]; Break[]], {x, 1, 100}], {n, 120}]][[2, 1]]
nkp[n_]:=Module[{k=1}, While[!And@@PrimeQ[{n+k, n*k+1}], k++]; k]; Array[nkp, 100] (* Harvey P. Dale, Apr 11 2012 *)
PROG
(PARI) a(n) = {my(k=1); while (!isprime(n+k) || !isprime(n*k+1), k++); k; } \\ Michel Marcus, May 14 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Jun 28 2003
EXTENSIONS
Corrected and extended by Zak Seidov, Jun 10 2006
STATUS
approved