|
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.
|
|
LINKS
|
T. D. Noe, Table of n, a(n) for n=1..691
R. J. Mathar, Maple programs to generate b005105.txt to b005108.txt, b081633.txt 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
|
njas, Simon Plouffe (plouffe(AT)math.uqam.ca)
|
|
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
|
