OFFSET
1,1
COMMENTS
This sequence is motivated by the author's conjecture in the comments in A230040.
Conjecture: a(n) < 2*n for all n > 2.
LINKS
Zhi-Wei Sun, Table of n, a(n) for n = 1..2000
EXAMPLE
a(1) = 3 since 3 = 1 + 1 + 1, and 6*1-1=5 is a Sophie Germain prime.
a(7) = 10 since 10 = 1 + 2 + 7, and 6*1-1=5, 6*2-1=11, 6*7-1=41, 6*1*2-1=11, 6*1*7-1=41, 6*2*7-1=83 are Sophie Germain primes.
MATHEMATICA
m=0
SQ[n_]:=SQ[n]=PrimeQ[n]&&PrimeQ[2n+1]
Do[Do[If[SQ[6i-1]&&SQ[6j-1]&&SQ[6(n-i-j)-1]&&SQ[6i*j-1]&&SQ[6*i(n-i-j)-1]&&SQ[6*j(n-i-j)-1],
m=m+1; Print[m, " ", n]; Goto[aa]], {i, 1, n/3}, {j, i, (n-i)/2}];
Label[aa]; Continue, {n, 1, 102}]
sgpQ[{x_, y_, z_}]:=AllTrue[{6x-1, 6y-1, 6z-1, 6x y-1, 6x z-1, 6y z-1, 2(6x-1)+1, 2(6y-1)+1, 2(6z-1)+ 1, 2(6x y-1)+1, 2(6x z-1)+1, 2(6y z-1)+1}, PrimeQ]; Select[Total/@Select[Tuples[Range[100], 3], sgpQ]//Union, #<110&] (* Harvey P. Dale, Jul 23 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Oct 07 2013
STATUS
approved