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%I #17 Nov 11 2019 09:29:10
%S 4,6,9,10,14,15,21,25,26,34,35,38,39,49,51,57,65,74,85,91,95,111,119,
%T 133,146,169,185,194,218,219,221,247,259,289,291,323,326,327,361,365,
%U 386,481,485,489,511,514,545,579,629,679,703,763,771,815,866,949,965
%N Semi-Pierpont semiprimes: products of exactly two Pierpont primes A005109.
%C 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 Vincenzo Librandi, <a href="/A113433/b113433.txt">Table of n, a(n) for n = 1..498</a>
%H Chris Caldwell, <a href="http://groups.yahoo.com/group/primeform/message/6588/">"Pierpont primes." primeform posting, Oct 25, 2005.</a>
%H Chris Caldwell, <a href="/A113433/a113433.pdf">"Pierpont primes." primeform posting, Oct 25, 2005.</a> [Cached copy]
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PierpontPrime.html">Pierpont Prime</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Semiprime.html">Semiprime</a>
%F {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 a(1) = 4 = 2^2 = [(2^0)*(3^0)+1]*[(2^1)*(3^0)+1] = A005109(1)*A005109(1).
%e a(2) = 6 = 2*3 = [(2^0)*(3^0)+1]*[(2^1)*(3^0)+1] = A005109(1)*A005109(2).
%e a(3) = 9 = 3^2 = [(2^1)*(3^0)+1]*[(2^1)*(3^0)+1] = A005109(2)*A005109(2).
%e a(4) = 10 = 2*5 = [(2^0)*(3^0)+1]*[(2^2)*(3^0)+1] = A005109(1)*A005109(3).
%e a(5) = 14 = 2*7 = [(2^0)*(3^0)+1]*[(2^1)*(3^1)+1] = A005109(1)*A005109(4).
%e a(6) = 15 = 3*5 = [(2^1)*(3^0)+1]*[(2^2)*(3^0)+1] = A005109(2)*A005109(3).
%t Select[Range[10^3], Plus @@ Last /@ FactorInteger[ # ] == 2 && And @@ (Max @@ First /@ FactorInteger[ # - 1] < 5 &) /@ First /@ FactorInteger[ # ] &] (* _Ray Chandler_, Jan 24 2006 *)
%Y Cf. A001358, A003586, A005109, A055600, A111153, A111206, A113432, A113434.
%K easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Nov 01 2005
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