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 A208281 Numbers n such that 3*prime(n)*2^k - 1 is prime for some k > 0 and then 3*prime(n)*2^k + 1 is also prime. 1
 1, 2, 3, 4, 6, 7, 9, 15, 24, 27, 28, 33, 34, 35, 58, 60, 61, 65, 67, 68, 69, 74, 78, 81, 86, 91, 92, 96, 105, 106, 108, 110, 119, 121, 125, 128, 129, 133, 134, 135, 137, 138, 146, 155, 172, 173, 174, 177, 179, 187, 199, 215, 216, 224 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Note that only first k for which 3*prime(n)*2^k - 1 is prime is used to test whether 3*prime(n)*2^k + 1 is prime. LINKS Pierre CAMI, Table of n, a(n) for n = 1..6836 EXAMPLE 3*prime(1)*2^1-1=11 prime,13 prime so a(1)=1 3*prime(2)*2^1-1=17 prime,19 prime so a(2)=2 3*prime(3)*2^1-1=29 prime,31 prime so a(3)=3 3*prime(4)*2^1-1=41 prime,43 prime so a(4)=4 3*prime(5)*2^1-1=65 composite 3*prime(5)*2^2-1=131 prime,133 composite 3*prime(6)*2^1-1=77 composite 3*prime(6)*2^2-1=155 composite 3*prime(6)*2^3-1=311 prime,313 prime so a(5)=6 MATHEMATICA t = {}; Do[p = Prime[n]; k = 1; While[! PrimeQ[3*p*2^k - 1], k++]; If[PrimeQ[3*p*2^k + 1], AppendTo[t, n]], {n, 224}]; t (* T. D. Noe, Feb 29 2012 *) PROG PFGW64 from Primeform group and SCRIPTIFY Command pfgw64 -f in.txt in.txt file : SCRIPT DIM nn, 0 DIM kk DIMS tt OPENFILEOUT myfile, k.txt LABEL loopn SET nn, nn+1 IF nn>50000 THEN END SET kk, 0 LABEL loopk SET kk, kk+1 SETS tt, %d, %d\,; nn; kk PRP 3*p(nn)*2^kk-1, tt IF ISPRP THEN GOTO a IF ISPRIME THEN GOTO a GOTO loopk LABEL a PRP 3*p(nn)*2^kk+1, tt IF ISPRP THEN GOTO b IF ISPRIME THEN GOTO b GOTO loopn LABEL b WRITE myfile, tt GOTO loopn CROSSREFS Cf. A207572. Sequence in context: A064414 A224482 A002475 * A306074 A250252 A246274 Adjacent sequences:  A208278 A208279 A208280 * A208282 A208283 A208284 KEYWORD nonn AUTHOR Pierre CAMI, Feb 25 2012 STATUS approved

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Last modified December 2 20:25 EST 2021. Contains 349445 sequences. (Running on oeis4.)