A226943 - OEIS

%I #35 Aug 20 2017 23:19:13

%S 4,14,314,141,15,415,1415,9,159,6,26,926,5926,15926,65,265,2653,92653,

%T 592653,35,535,6535,5926535,58,358,265358,314159265358,589,3589,53589,

%U 2653589,92653589,1592653589,1415926535897,979,5358979,59265358979,159265358979

%N Semiprimes in the order in which they appear in the decimal expansion of Pi.

%C This is to semiprimes A001358 as A198019 is to primes A000040. Considering the first 1, 2, 3, 4, ... digits of the decimal expansion 3.14159... of Pi, record the semiprimes that have not occurred earlier, the smaller first if two or more appear by the n-th digit that have not been seen in the first n-1 digits.

%H Giovanni Resta, <a href="/A226943/b226943.txt">Table of n, a(n) for n = 1..300</a>

%e There are no semiprimes in the first 1 or 2 digits (3, 31). Then after 3 digits we have three: 4, 14, and 314 appearing for the first time. So a(1) = 4, a(2) = 14 and a(3) = 314.

%t semiQ[n_] := Total[Last /@ FactorInteger@n ] == 2; sp = Select[Range@ 999, semiQ]; spQ[n_] := If[n < 10^6, semiQ@n, ! Or @@ IntegerQ /@ (n/sp) && semiQ@ n]; seq = {}; Do[seq = Join[seq, Select[Union@ Complement[ Mod[FromDigits@ RealDigits[Pi, 10, n][[1]], 10^Range[n, 1, -1]], seq], spQ]], {n, 30}]; seq (* _Giovanni Resta_, Oct 01 2013 *)

%Y Cf. A000796, A001358, A198019.

%K nonn,base

%O 1,1

%A _Jonathan Vos Post_, Sep 01 2013