cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A209600 Analog of A048613 based on sum of reciprocals of Mersenne primes.

Original entry on oeis.org

1, 3, 2, 16, 17, 21, 24, 26, 29, 412, 788, 1045, 369625, 369636
Offset: 1

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Author

N. J. A. Sloane, Mar 10 2012

Keywords

Links

Crossrefs

Cf. A048613, A173898, A000668, A209601.

A059101 Number of terms of the fractional part of A001203 for which the geometric mean produces increasingly better approximations to Khinchin's constant.

Original entry on oeis.org

1, 3, 7, 8, 9, 10, 11, 15, 16, 17, 97, 100, 103, 117, 976, 32307, 32760, 32787, 60508, 60601, 60663, 187154, 230084, 1120375, 1146529, 2211732, 4497058, 1434927965, 1434935064, 1434935232, 1434935281, 1471575921, 1471636101, 1490844937, 1491643951, 1498931686
Offset: 1

Views

Author

Hans Havermann, Feb 13 2001

Keywords

Comments

Next term > 3*10^10. - Hans Havermann, Jul 29 2024
The geometric mean of 1498931686 terms is Khinchin + 1.00240496*10^-13.

Examples

			The geometric mean of 17 terms (Khinchin + 0.00752006) is not bettered until we calculate the geometric mean of 97 terms (Khinchin - 0.00326655).

Links

Crossrefs

Cf. A001203, A048613.

Formula

p = Rest[{A001203}]; q = N[1, 100]; r = p[[1]] + 1; t = {}; Do[q = q*p[[i]]; g = q^(1/i) - Khinchin; If[Abs[g] < r, r = Abs[g]; t = Append[t, i]], {i, 1, Length[p]}]; t

Extensions

a(28)-a(36) from Hans Havermann, Dec 27 2012

A059102 Number of terms of the fractional part of A030168 for which the geometric mean produces increasingly better approximations to Khinchin's constant.

Original entry on oeis.org

1, 9, 10, 12, 13, 26, 48, 49, 51, 65, 66, 67, 1330, 1331, 1332, 1336, 1337, 1338, 1339, 1340, 1431, 5666, 10331, 537086, 537095, 538045, 576768, 576789
Offset: 1

Views

Author

Hans Havermann, Feb 13 2001

Keywords

Comments

Next term > 3307254.

Examples

			The geometric mean of 67 terms (Khinchin + 0.0128639) is not bettered until we calculate the geometric mean of 1330 terms (Khinchin + 0.011153).

Crossrefs

Cf. A030168, A048613.

Formula

p = Drop[{A030168}, 1]; q = N[1, 100]; r = p[[1]] + 1; t = {}; Do[q = q*p[[i]]; g = q^(1/i) - Khinchin; If[Abs[g] < r, r = Abs[g]; t = Append[t, i]], {i, 1, Length[p]}]; t
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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