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A129112 Decimal expansion of constant equal to concatenated semiprimes.

%I A129112 #11 Feb 16 2025 08:33:05
%S A129112 4,6,9,1,0,1,4,1,5,2,1,2,2,2,5,2,6,3,3,3,4,3,5,3,8,3,9,4,6,4,9,5,1,5,
%T A129112 5,5,7,5,8,6,2,6,5,6,9,7,4,7,7,8,2,8,5,8,6,8,7,9,1,9,3,9,4,9,5,1,0,6,
%U A129112 1,1,1,1,1,5,1,1,8,1,1,9,1,2,1,1,2,2,1,2,3,1,2,9
%N A129112 Decimal expansion of constant equal to concatenated semiprimes.
%C A129112 Is this, as Copeland and Erdos (1946) showed for the Copeland-Erdos constant, a normal number in base 10? I conjecture that it is, despite the fact that the density of odd semiprimes exceeds the density of even semiprimes. What are the first few digits of the continued fraction of this constant? What are the positions of the first occurrence of n in the continued fraction? What are the incrementally largest terms and at what positions do they occur?
%C A129112 Coincides up to n=15 with concatenation of A046368. - M. F. Hasler, Oct 01 2007
%C A129112 Indeed, a theorem of Copeland & Erdős proves that this constant is 10-normal. - _Charles R Greathouse IV_, Feb 06 2015
%H A129112 A. H. Copeland and P. Erdős, <a href="http://www.renyi.hu/~p_erdos/1946-01.pdf">Note on normal numbers</a>, Bull. Amer. Math. Soc. 52 (1946), pp. 857-860.
%H A129112 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Copeland-ErdosConstant.html">Copeland-Erdos Constant.</a>
%e A129112 4.691014152122252633343538394649515557586265...
%t A129112 Flatten[IntegerDigits/@Select[Range[200],PrimeOmega[#]==2&]] (* _Harvey P. Dale_, Jan 17 2012 *)
%o A129112 (PARI) print1(4); for(n=6,129, if(bigomega(n)==2, d=digits(n); for(i=1,#d, print1(", "d[i])))) \\ _Charles R Greathouse IV_, Feb 06 2015
%Y A129112 Cf. A001358, A019518, A030168, A033308 = decimal expansion of Copeland-Erdos constant: concatenate primes, A033309-A033311, A129808.
%K A129112 base,cons,easy,nonn
%O A129112 1,1
%A A129112 _Jonathan Vos Post_, May 24 2007