Search: id:A005109
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%I A005109 M0673
%S A005109 2,3,5,7,13,17,19,37,73,97,109,163,193,257,433,487,577,769,1153,1297,
%T A005109 1459,2593,2917,3457,3889,10369,12289,17497,18433,39367,52489,65537,
%U A005109 139969,147457,209953,331777,472393,629857,746497,786433,839809,995329
%N A005109 Class 1- (or Pierpont) primes: primes of the form 2^t*3^u + 1.
%C A005109 Gleason, p. 191: a regular polygon of n sides can be constructed by ruler, 
               compass and angle-trisector iff n = 2^r * 3^s * p_1 * p_2 .... p_k, 
               where p_1, p_2,....,p_k are distinct elements of this sequence and 
               >3.
%C A005109 Sequence gives primes solutions to p==+1 (mod phi(p-1)) - Benoit Cloitre 
               (benoit7848c(AT)orange.fr), Feb 22 2002
%D A005109 D. A. Cox and J. Shurman, Geometry and number theory on clovers, Amer. 
               Math. Monthly, 112 (2005), 682-704.
%D A005109 Andrew M. Gleason: Angle Trisection, the Heptagon and the Triskaidecagon. 
               American Mathematical Monthly 95 (1988) 185 - 194.
%D A005109 R. K. Guy, Unsolved Problems in Number Theory, A18.
%D A005109 George E. Martin: Geometric Constructions. Springer, 1998. ISBN 0-387-98276-0.
%D A005109 James Pierpont: On an Undemonstrated Theorem of the Disquisitiones Aritmeticae. 
               American Mathematical Society Bulletin 2 (1895-1896) 77 - 83.
%D A005109 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A005109 T. D. Noe, <a href="b005109.txt">Pierpont primes less than 10^100; table 
               of n, a(n) for n = 1..795</a>
%H A005109 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PierpontPrime.html">Pierpont Prime</a>
%F A005109 A122257(a(n)) = 1; A122258(n) = number of Pierpont primes <= n; A122260 
               gives numbers having only Pierpont primes as factors. - Reinhard 
               Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 29 2006
%e A005109 97 = 2^5*3 + 1 is a member.
%t A005109 Take[ Select[ Sort[ Flatten[ Table[2^t*3^u + 1, {t, 0, 22}, {u, 0, 16}]]], 
               PrimeQ[ # ] &], 42] (* or *)
%t A005109 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]]; ClassMinusNbr[n_] := Length[NestWhileList[f, n, UnsameQ, All]] 
               - 3; Prime[ Select[ Range[3, 6300], ClassMinusNbr[ Prime[ # ]] == 
               1 &]]
%t A005109 Select[Prime /@ Range[10^5], Max @@ First /@ FactorInteger[ # - 1] < 
               5 &] (Ray Chandler (rayjchandler(AT)sbcglobal.net), Nov 01 2005)
%Y A005109 Cf. A048135, A048136, A056637, A005105, A005110, A005111, A005112, A081424, 
               A081425, A081426, A081427, A081428, A081429, A081430.
%Y A005109 Cf. A122259.
%Y A005109 Sequence in context: A109461 A138539 A090422 this_sequence A080608 A137812 
               A094317
%Y A005109 Adjacent sequences: A005106 A005107 A005108 this_sequence A005110 A005111 
               A005112
%K A005109 nonn,nice,easy
%O A005109 1,1
%A A005109 N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
%E A005109 Comments and additional references from Antreas P. Hatzipolakis (xpolakis(AT)otenet.gr). 
               More terms from David W. Wilson (davidwwilson(AT)comcast.net)
%E A005109 More terms from Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 22 2002
%E A005109 More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Mar 20 2003

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