A033309 -id:A033309 - cp's OEIS frontend

A033310 Incrementally largest terms in continued fraction for Copeland-Erdős constant.

0, 4, 8, 16, 18, 58, 87, 484, 1468, 3955, 6986, 17474, 26174, 37084, 73646, 89141, 187645, 542374, 551071, 644045, 925191, 2037817, 4576230, 13320898, 16917960, 190435991, 230132891, 407588556

Offset: 1

Eric W. Weisstein

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

Cf. A033308, A033309, A030168.
Cf. A224890 (positions of incrementally largest terms).
Cf. A030168 (continued fraction for Copeland-Erdős constant).

Extended by Eric W. Weisstein, Mar 25 2009

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

A033311 Positions of incrementally largest terms in continued fraction for Copeland-Erdős constant.

Original entry on oeis.org

1, 2, 4, 5, 6, 18, 36, 72, 89, 1557, 3728, 4730, 27642, 60322, 90720, 104378, 107183, 241453, 453796, 679114, 901262, 934243, 1298092, 5996127, 7360332, 76543031, 299039550, 382621530

Offset: 1

Eric W. Weisstein

This version uses an incorrect c.f. term indexing of [a_1; a_2, ...] instead of [a_0; a_1, ...]; see A224890 for correctly indexed version.

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

Cf. A033308, A033309, A033310, A030168.

Cf. A224890 (= a(n) - 1).

a(n) = A224890(n) + 1.

More terms from Eric W. Weisstein, Mar 25 2009

A224891 Position of first occurrence of n in continued fraction for Copeland-Erdos constant.

Original entry on oeis.org

7, 15, 19, 1, 6, 14, 11, 3, 16, 253, 97, 153, 52, 211, 252, 4, 82, 5, 63, 352, 1048, 554, 561, 689, 87, 333, 53, 1794, 620, 391, 1100, 1202, 714, 3928, 627, 137, 256, 647, 28, 328, 58, 2416, 443, 1352, 341, 1347, 910, 3042, 3869, 839, 989, 680, 228, 688, 748, 2310, 8253, 17

Offset: 1

Eric W. Weisstein, Jul 24 2013

nonn

Correctly indexed version of A033309.

Smallest numbers not occurring in the first 1,011,597,392 terms of the c.f. are 14731, 15456, 15579, 15869, ...

Eric W. Weisstein, Table of n, a(n) for n = 1..14730
Eric Weisstein's World of Mathematics, Copeland-Erdos Constant Continued Fraction

Cf. A033309 (= a(n) + 1).

Cf. A030168 (continued fraction of the Copeland-Erdos constant).

a(n) = A033309(n) - 1.

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

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A033310 Incrementally largest terms in continued fraction for Copeland-Erdős constant.

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A033311 Positions of incrementally largest terms in continued fraction for Copeland-Erdős constant.

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A224891 Position of first occurrence of n in continued fraction for Copeland-Erdos constant.

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A129112 Decimal expansion of constant equal to concatenated semiprimes.

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