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A227938
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List of those numbers which can be written as x + y + z (x, y, z > 0) such that all the six numbers 6*x-1, 6*y-1, 6*z-1, 6*x*y-1, 6*x*z-1 and 6*y*z-1 are Sophie Germain primes.
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2
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3, 4, 5, 6, 7, 9, 10, 11, 15, 16, 17, 18, 19, 20, 21, 24, 25, 28, 31, 32, 33, 34, 35, 41, 42, 44, 45, 46, 47, 49, 51, 53, 55, 58, 61, 62, 63, 64, 65, 66, 72, 74, 75, 76, 77, 78, 79, 80, 84, 86, 87, 88, 89, 90, 91, 92, 93, 94, 101, 102
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OFFSET
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1,1
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COMMENTS
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This sequence is motivated by the author's conjecture in the comments in A230040.
Conjecture: a(n) < 2*n for all n > 2.
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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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}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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