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A120225
a(n) is the minimal number k>n such that n+k and n*k+1 are primes.
6
2, 3, 4, 7, 6, 7, 10, 9, 14, 13, 18, 19, 24, 15, 16, 21, 24, 29, 22, 21, 22, 31, 30, 43, 28, 33, 34, 39, 32, 41, 36, 39, 34, 37, 66, 43, 60, 41, 50, 43, 42, 55, 46, 53, 52, 51, 50, 59, 52, 51, 56, 55, 56, 55, 58, 75, 74, 69, 68, 67, 66, 75, 74, 67, 86, 83, 70, 89, 70, 79, 102, 79
OFFSET
1,1
COMMENTS
Differs from A120224 in the first term.
LINKS
EXAMPLE
a(3)=4 because 3+4=7 and 3*4+1=13 are prime;
a(8)=9 because 8+9=17 and 8*9+1=73 are prime,
MATHEMATICA
Reap[Do[Do[If[PrimeQ[{n+x, n*x+1}]=={True, True}, Sow[x]; Break[]], {x, n+1, 1000}], {n, 120}]][[2, 1]]
mnk[n_]:=Module[{k=n+1}, While[!AllTrue[{n+k, n*k+1}, PrimeQ], k++]; k]; Array[ mnk, 80] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 15 2015 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Zak Seidov, Jun 10 2006
STATUS
approved