A033311 -id:A033311 - cp's OEIS frontend

A224890 Positions of incrementally largest terms in continued fraction for Copeland-Erdős constant.

0, 1, 3, 4, 5, 17, 35, 71, 88, 1556, 3727, 4729, 27641, 60321, 90719, 104377, 107182, 241452, 453795, 679113, 901261, 934242, 1298091, 5996126, 7360331, 76543030, 299039549, 382621529

Offset: 1

Eric W. Weisstein, Jul 24 2013

Correctly indexed version of A033311.

			The c.f. of the Copeland-Erdős constant is [a_0; a_1, a_2, ...] = [0; 4, 4, 8, 16, 18, 5, 1, ...], so record terms occur at positions 0, 1, 3, 4, 5, ...

Eric Weisstein's World of Mathematics, Copeland-Erdős Constant Continued Fraction

Cf. A033311 (= a(n) + 1).
Cf. A033310 (incrementally largest terms).
Cf. A030168 (continued fraction for Copeland-Erdős constant).

a(n) = A033311(n) - 1.

a(25)-a(28) from Eric W. Weisstein, Jul 24 2013

A129112 Decimal expansion of constant equal to concatenated semiprimes.

Original entry on oeis.org

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

Jonathan Vos Post, May 24 2007

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

			4.691014152122252633343538394649515557586265...

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.

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

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

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

cp's OEIS Frontend

A224890 Positions of incrementally largest terms in continued fraction for Copeland-Erdős constant.

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