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.

A222754 Least odd number k such that difference between halving and tripling steps in Collatz (3x+1) trajectory of k is n, or 0 if there is no such k.

Original entry on oeis.org

1, 0, 0, 3, 0, 13, 7, 9, 19, 25, 33, 43, 39, 79, 105, 135, 123, 169, 159, 295, 283, 111, 223, 297, 175, 103, 91, 121, 31, 27, 55, 73, 97, 129, 171, 231, 313, 411, 543, 327, 649, 859, 763, 1017, 1351, 1215, 703, 937, 871, 1161, 2223, 3097, 2631, 3567, 3175, 4233
Offset: 0

Views

Author

T. D. Noe, Mar 04 2013

Keywords

Links

Crossrefs

Cf. A222752, A222753, A222755.

Programs

  • Mathematica
    Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; nn = 51; t = Table[0, {nn}]; n = -1; While[Min[Drop[t, 5]] == 0, n = n + 2; c = Collatz[n]; e = Select[c, EvenQ]; diff = 2*Length[e] - Length[c]; If[diff < nn - 1 && t[[diff + 2]] == 0, t[[diff + 2]] = n]]; t

A222753 Number of odd numbers k such that difference between halving and tripling steps in Collatz (3x+1) trajectory of k is n.

Original entry on oeis.org

1, 0, 0, 2, 0, 2, 3, 6, 6, 9, 11, 19, 28, 43, 66, 98, 145, 219, 327, 474, 744, 1125, 1673, 2481, 3723, 5600, 8415, 12630, 18863, 28395, 42620, 63907
Offset: 0

Views

Author

T. D. Noe, Mar 04 2013

Keywords

Comments

See A222752 for the rows of numbers.

Crossrefs

Cf. A222752, A222754, A222755.

Programs

  • Mathematica
    Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; nn = 15; t = Table[0, {nn}]; Do[c = Collatz[n]; e = Select[c, EvenQ]; diff = 2*Length[e] - Length[c]; If[diff < nn - 1, t[[diff + 2]]++], {n, 1, 2^(nn - 1), 2}]; t

A222755 Greatest odd number k such that difference between halving and tripling steps in Collatz (3x+1) trajectory of k is n, or 0 if there is no such k.

Original entry on oeis.org

1, 0, 0, 5, 0, 21, 17, 85, 113, 341, 453, 1365, 1813, 5461, 7281, 21845, 29125, 87381, 116501, 349525, 466033, 1398101, 1864133, 5592405, 7456533, 22369621, 29826161, 89478485, 119304645, 357913941, 477218581, 1431655765
Offset: 0

Views

Author

T. D. Noe, Mar 04 2013

Keywords

Comments

Note that a(n) <= 2^n, with equality only for n = 0.

Crossrefs

Cf. A222752, A222753, A222754.

Programs

  • Mathematica
    Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; nn = 15; t = Table[0, {nn}]; Do[c = Collatz[n]; e = Select[c, EvenQ]; diff = 2*Length[e] - Length[c]; If[diff < nn - 1, t[[diff + 2]] = n], {n, 1, 2^(nn - 1), 2}]; t

Extensions

a(31) added - T. D. Noe, Mar 05 2013
Showing 1-3 of 3 results.

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

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