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 1-4 of 4 results.

A355240 Numbers of steps until the Collatz iteration started at k > 4 returns to either k-1 or k+1.

Original entry on oeis.org

3, 8, 13, 44, 75, 88, 101, 119
Offset: 1

Views

Author

Hugo Pfoertner, Jul 04 2022

Keywords

Comments

It is conjectured that no further terms exist.
Michael S. Branicky checked this up to 2*10^9 and found no starting values other than the 74 terms given in A355239 and also in the attached file.
The terms of this sequence are expected to be close to the sum of numerators and denominators in a rational approximation of log(2)/log(3). See A355514, which shares terms 3, 8, 13, 44, 75.

Links

Crossrefs

Cf. A005186, A006577, A355514.
A355239 gives the list of starting values.
Cf. A355568, A355569.

Programs

  • PARI
    a355240(upto) = {my(D=List()); for (start=5, upto, my(old=start,new=0,L=0);while (abs(new-start)>1 && new!=1, L++; if(old%2==0,new=old/2,new=3*old+1);old=new); if(new>1, listput(~D,L))); Set(D)};
a355240(10000)

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.

A355513 Sum of numerator and denominator in a rational approximation j/k of q = log(2)/log(3), such that abs(j/k - q) is a new minimum.

Original entry on oeis.org

2, 3, 5, 8, 13, 18, 31, 75, 106, 137, 517, 654, 791, 928, 1719, 21419, 23138, 24857, 26576, 28295, 30014, 31733, 33452, 35171, 36890, 38609, 40328, 82375, 205078, 287453, 492531, 14078321, 14570852, 15063383, 15555914, 16048445, 16540976, 17033507, 17526038, 18018569
Offset: 1

Views

Author

Hugo Pfoertner, Jul 05 2022

Keywords

Crossrefs

Cf. A102525, A355512, A355514, A355515.

Programs

  • PARI
    a355513(upto) = {my(q=log(2)/log(3), dmin=oo);for (m=1, upto, my(n=round(m*q), qq=n/m, d=abs(qq-q)); if(d

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 1-4 of 4 results.

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

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