Search: id:A113433
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%I A113433
%S A113433 4,6,9,10,14,15,21,25,26,34,35,38,39,49,51,57,65,74,85,91,95,111,119,
%T A113433 133,146,169,185,194,218,219,221,247,259,289,291,323,326,327,361,365,
%U A113433 386,481,485,489,511,514,545,579,629,679,703,763,771,815,866,949,965
%N A113433 Semi-Pierpont semiprimes: products of exactly two Pierpont primes A005109.
%C A113433 Semiprime both of whose prime factors are Pierpont primes (A005109), 
               which are primes of the form (2^K)*(3^L)+1. Not to be confused with 
               A113432: Pierpont semiprimes [Semiprimes of the form (2^K)*(3^L)+1]. 
               This terminology itself is by analogy to what Tomaszewski used for 
               the Sophie Germain counterparts A111153 and A111206.
%H A113433 Caldwell, C., <a href="http://groups.yahoo.com/group/primeform/message/
               6588/">"Pierpont primes." primeform posting, Oct 25, 2005.</a>
%H A113433 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PierpontPrime.html">Pierpont Prime</a>
%H A113433 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Semiprime.html">Semiprime</a>
%F A113433 {a(n)} = Semiprimes A001358 both of whose factors are of the form (2^K)*(3^L)+1. 
               {a(n)} = {A005109(i)*A005109(j) for integers i and j not necessarily 
               distinct}.
%e A113433 a(1) = 4 = 2^2 = [(2^0)*(3^0)+1]*[(2^1)*(3^0)+1] = A005109(1)*A005109(1).
%e A113433 a(2) = 6 = 2*3 = [(2^0)*(3^0)+1]*[(2^1)*(3^0)+1] = A005109(1)*A005109(2).
%e A113433 a(3) = 9 = 3^2 = [(2^1)*(3^0)+1]*[(2^1)*(3^0)+1] = A005109(2)*A005109(2).
%e A113433 a(4) = 10 = 2*5 = [(2^0)*(3^0)+1]*[(2^2)*(3^0)+1] = A005109(1)*A005109(3).
%e A113433 a(5) = 14 = 2*7 = [(2^0)*(3^0)+1]*[(2^1)*(3^1)+1] = A005109(1)*A005109(4).
%e A113433 a(6) = 15 = 3*5 = [(2^1)*(3^0)+1]*[(2^2)*(3^0)+1] = A005109(2)*A005109(3).
%t A113433 Select[Range[10^3], Plus @@ Last /@ FactorInteger[ # ] == 2 && And @@ 
               (Max @@ First /@ FactorInteger[ # - 1] < 5 &) /@ First /@ FactorInteger[ 
               # ] &] (*Chandler*)
%Y A113433 Cf. A001358, A003586, A005109, A055600, A111153, A111206, A113432, A113434.
%Y A113433 Sequence in context: A108574 A157931 A046368 this_sequence A115654 A036326 
               A078972
%Y A113433 Adjacent sequences: A113430 A113431 A113432 this_sequence A113434 A113435 
               A113436
%K A113433 easy,nonn
%O A113433 1,1
%A A113433 Jonathan Vos Post (jvospost3(AT)gmail.com), Nov 01 2005

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