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.

A355514 Sum of numerator and denominator in a rational approximation j/k of q = log(2)/log(3), such that q - j/k is a new minimum, i.e., q is approximated from below.

Original entry on oeis.org

1, 3, 8, 13, 44, 75, 106, 243, 380, 517, 654, 791, 2510, 4229, 5948, 7667, 9386, 11105, 12824, 14543, 16262, 17981, 19700, 21419, 23138, 24857, 26576, 28295, 30014, 31733, 33452, 35171, 36890, 38609, 40328, 122703, 205078, 492531, 27869189, 166722603, 305576017
Offset: 1

Views

Author

Hugo Pfoertner, Jul 05 2022

Keywords

Crossrefs

Cf. A102525, A355512, A355513, A355515.
Terms are candidates for being in A355240, which shares 3, 8, 13, 44, 75.

Programs

  • PARI
    a355514(upto) = {my(q=log(2)/log(3), dmin=oo);for (m=1, upto, my(n=floor(m*q), qq=n/m, d=q-qq); if (d

A355512 Sum of numerator and denominator in the convergents of the approximation of log(2)/log(3) by a continued fraction.

Original entry on oeis.org

2, 3, 5, 13, 31, 106, 137, 791, 1719, 40328, 82375, 205078, 287453, 492531, 27376658, 27869189, 138853414, 444429431, 583282845, 1027712276, 15998966985, 17026679261, 169239080334, 355504839929, 1946763279979, 13982847799782, 15929611079761, 29912458879543, 135579446597933
Offset: 1

Views

Author

Hugo Pfoertner, Jul 05 2022

Keywords

Crossrefs

Cf. A005663, A005664, A102525, A355513, A355515.
Cf. A355514 for the relation to potential cycle lengths of the 3x+1 problem.

Programs

  • PARI
    a355512(upto) = {my(q=log(2)/log(3), fa=oo); for (denmax=1, upto, my(f=bestappr(q,denmax)); if (fa!=f, print1(numerator(f)+denominator(f),", "); fa=f))};
\\ needs increased precision for larger terms
a355512(10^6)
  • PARI
    \\ See also A005663 and A005664 for efficient code.

A355515 Sum of numerator and denominator in a rational approximation j/k of q = log(2)/log(3), such that j/k - q is a new minimum, i.e., q is approximated from above.

Original entry on oeis.org

2, 5, 18, 31, 137, 928, 1719, 42047, 82375, 287453, 779984, 1272515, 1765046, 2257577, 2750108, 3242639, 3735170, 4227701, 4720232, 5212763, 5705294, 6197825, 6690356, 7182887, 7675418, 8167949, 8660480, 9153011, 9645542, 10138073, 10630604, 11123135, 11615666, 12108197
Offset: 1

Views

Author

Hugo Pfoertner, Jul 05 2022

Keywords

Crossrefs

Cf. A102525, A355512, A355513, A355514.

Programs

  • PARI
    a355515(upto) = {my(q=log(2)/log(3), dmin=oo); for (m=1, upto, my(n=ceil(m*q), qq=n/m, d=qq-q); if (d
Showing 1-3 of 3 results.

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

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