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A005105
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Primes of the form 2^i*3^j - 1 with i, j >= 0.
(Formerly M0665)
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41
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2, 3, 5, 7, 11, 17, 23, 31, 47, 53, 71, 107, 127, 191, 383, 431, 647, 863, 971, 1151, 2591, 4373, 6143, 6911, 8191, 8747, 13121, 15551, 23327, 27647, 62207, 73727, 131071, 139967, 165887, 294911, 314927, 442367, 472391, 497663, 524287, 786431, 995327
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Class 1+ primes.
Odd terms are primes satisfying p==-1 (mod phi(p+1)). - Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 22 2002
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REFERENCES
| G. Everest, P. Rogers and T. Ward, A higher-rank Mersenne problem, pp. 95-107 of ANTS 2002, Lect. Notes Computer Sci. 2369 (2002).
R. K. Guy, Unsolved Problems in Number Theory, A18.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| R. J. Mathar, Maple programs to generate b-files for b005105 to b005108, b081633 etc.
Charles R Greathouse IV, Table of n, a(n) for n = 1..5000, replacing an earlier b-file from T. D. Noe
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MAPLE
| For Maple program see Mathar link.
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MATHEMATICA
| Take[ Select[ Sort[ Flatten[ Table[2^t*3^u - 1, {t, 0, 22}, {u, 0, 16}]]], PrimeQ[ # ] &], 43] (* or *)
Prime[ Select[ Range[78200], Mod[ Prime[ # ] + 1, EulerPhi[ Prime[ # ] + 1]] == 0 &]] (* or *)
PrimeFactors[n_Integer] := Flatten[ Table[ #[[1]], {1}] & /@ FactorInteger[n]]; f[n_Integer] := Block[{m = n}, If[m == 0, m = 1, While[ IntegerQ[m/2], m /= 2]; While[ IntegerQ[m/3], m /= 3]]; Apply[Times, PrimeFactors[m] + 1]]; ClassPlusNbr[n_] := Length[ NestWhileList[f, n, UnsameQ, All]] - 3; Prime[ Select[ Range[3, 78200], ClassPlusNbr[ Prime[ # ]] == 1 &]]
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PROG
| (PARI) list(lim)=my(v=List(), N); for(n=0, log(lim)\log(3), N=3^n; while(N<=lim, if(ispseudoprime(N-1), listput(v, N-1)); N<<=1)); vecsort(Vec(v)) \\ Charles R Greathouse IV, Jul 15 2011
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CROSSREFS
| Cf. A069353, A069356, A005109, A005113, A005106, A005107, A005108.
Sequence in context: A040089 A113161 A038953 * A086566 A188552 A104892
Adjacent sequences: A005102 A005103 A005104 * A005106 A005107 A005108
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
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EXTENSIONS
| More terms from Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 22 2002
Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Mar 20 2003
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