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

Offset: 1

Author

Jonathan Vos Post, May 24 2007

Keywords

• base
• cons
• easy
• nonn

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

Examples

			4.691014152122252633343538394649515557586265...
		

Links

• 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.

Crossrefs

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

Programs

Mathematica

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

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