A129112 - OEIS

A129112

Decimal expansion of constant equal to concatenated semiprimes.

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, 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, 1, 1, 1, 1, 1, 5, 1, 1, 8, 1, 1, 9, 1, 2, 1, 1, 2, 2, 1, 2, 3, 1, 2, 9

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OFFSET

1,1

COMMENTS

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?

Coincides up to n=15 with concatenation of A046368. - M. F. Hasler, Oct 01 2007

Indeed, a theorem of Copeland & Erdős proves that this constant is 10-normal. - Charles R Greathouse IV, Feb 06 2015

LINKS

Table of n, a(n) for n=1..92.

A. H. Copeland and P. Erdős, Note on normal numbers, Bull. Amer. Math. Soc. 52 (1946), pp. 857-860.

Eric Weisstein's World of Mathematics, Copeland-Erdos Constant.

EXAMPLE

4.691014152122252633343538394649515557586265...

MATHEMATICA

Flatten[IntegerDigits/@Select[Range[200], PrimeOmega[#]==2&]] (* Harvey P. Dale, Jan 17 2012 *)

PROG

(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

CROSSREFS

Cf. A001358, A019518, A030168, A033308 = decimal expansion of Copeland-Erdos constant: concatenate primes, A033309-A033311, A129808.

Sequence in context: A010478 A106146 A154521 * A239634 A175013 A210616

Adjacent sequences: A129109 A129110 A129111 * A129113 A129114 A129115

KEYWORD

base,cons,easy,nonn

AUTHOR

Jonathan Vos Post, May 24 2007

STATUS

approved