|
Search: id:A005105
|
|
|
| A005105 |
|
Primes of the form 2^i*3^j - 1 with i, j >= 0.
(Formerly M0665)
|
|
+0
32
|
|
| 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; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
Class 1+ primes.
Odd terms are primes satisfying p==-1 (mod phi(p+1)). - Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 22 2002
|
|
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).
|
|
LINKS
|
T. D. Noe, Table of n, a(n) for n=1..691
R. J. Mathar, Maple programs to generate b-files for b005105 to b005108, b081633 etc.
|
|
MAPLE
|
For Maple program see Mathar link.
|
|
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 &]]
|
|
CROSSREFS
|
Cf. A069353, A069356, A005109, A005113, A005106, A005107, A005108.
Sequence in context: A040089 A113161 A038953 this_sequence A086566 A104892 A065436
Adjacent sequences: A005102 A005103 A005104 this_sequence A005106 A005107 A005108
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
|
|
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
|
|
|
Search completed in 0.002 seconds
|
