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A242085
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Smallest k such that (2*k*3^n-1)*2*k*3^n-1 is prime, with k not divisible by 3.
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4
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1, 2, 1, 2, 14, 2, 8, 5, 4, 5, 4, 40, 5, 29, 5, 7, 5, 19, 13, 1, 37, 34, 13, 2, 1, 17, 13, 2, 7, 28, 34, 26, 61, 2, 41, 43, 2, 10, 118, 52, 4, 4, 11, 7, 20, 139, 35, 11, 4, 29, 40, 8, 44, 7, 64, 37, 47, 175, 14, 23, 142, 23, 5, 32, 104, 110, 4, 26, 47, 25
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OFFSET
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1,2
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COMMENTS
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Conjectures: the ratio a(n)/n is always <10 and sum(a(n)/n)/N for n=1 to N tends to 1 as N tends to infinity.
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LINKS
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EXAMPLE
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(1*2*3^1-1)*1*2*3^1-1=29 so a(1)=1.
(1*2*3^2-1)*1*2*3^2-1=305 composite, (2*2*3^2-1)*2*2*3^2-1=1259 prime so a(2)=2.
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MATHEMATICA
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sk[n_]:=Module[{k=1, c=2*3^n}, While[Divisible[k, 3]||!PrimeQ[(k*c-1) (k*c)-1], k++]; k]; Array[sk, 70] (* Harvey P. Dale, Aug 05 2014 *)
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PROG
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(PFGW & SCRIPT)
SCRIPT
DIM n, 0
DIM i
DIM pp
DIMS t
OPENFILEOUT myf, a(n).txt
LABEL loop1
SET n, n+1
SET i, 0
LABEL loop2
SET i, i+1
SETS t, %d, %d\,; n; i
SET pp, (2*i*3^n-1)*2*i*3^n-1
PRP pp, t
IF ISPRP THEN GOTO a
GOTO loop2
LABEL a
WRITE myf, t
GOTO loop1
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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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