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 1-6 of 6 results.

A133424 Analog of A060410 for the 5x+1 problem (cf. A133419).

Original entry on oeis.org

6, 66, 216, 366, 516, 666, 816, 1116, 2016, 4866, 5766, 8616, 9516, 229866, 286116, 473616, 737016, 3230766, 4438266, 6260016, 10637016, 107662496, 117661116, 152291166, 176254866, 179900766, 201566166, 230949516
Offset: 1

Views

Author

N. J. A. Sloane, Nov 27 2007

Keywords

Comments

The 5x+1 map sends x to x/2 if x is even, x/3 if x is divisible by 3, otherwise 5x+1.

Links

Crossrefs

Cf. A133419, A133423, A133419, ...

A133426 Analog of A060410 for the 7x+1 problem (cf. A133421).

Original entry on oeis.org

8, 50, 162, 470, 9584, 28400, 91890, 193040, 265070, 291824, 337100, 388830, 524070, 3231824, 18052070, 30949850, 31021880, 65552768, 774659600, 10276607888, 38128783428, 190067750300, 4835458627140, 25515567812750
Offset: 1

Views

Author

N. J. A. Sloane, Nov 27 2007

Keywords

Comments

The 7x+1 map sends x to x/2 if x is even, x/3 if x is divisible by 3, x/5 if x is divisible by 5, otherwise 7x+1.

Links

Crossrefs

Cf. A133421, A133425, A133419, ...

A006884 In the '3x+1' problem, these values for the starting value set new records for highest point of trajectory before reaching 1.

Original entry on oeis.org

1, 2, 3, 7, 15, 27, 255, 447, 639, 703, 1819, 4255, 4591, 9663, 20895, 26623, 31911, 60975, 77671, 113383, 138367, 159487, 270271, 665215, 704511, 1042431, 1212415, 1441407, 1875711, 1988859, 2643183, 2684647, 3041127, 3873535, 4637979, 5656191
Offset: 1

Views

Author

N. J. A. Sloane, Robert Munafo

Keywords

Comments

Both the 3x+1 steps and the halving steps are counted.
Where records occur in A025586: A006885(n) = A025586(a(n)) and A025586(m) < A006885(n) for m < a(n). - Reinhard Zumkeller, May 11 2013

References

  • R. B. Banks, Slicing Pizzas, Racing Turtles and Further Adventures in Applied Mathematics, Princeton Univ. Press, 1999. See p. 96.
  • D. R. Hofstadter, Goedel, Escher, Bach: an Eternal Golden Braid, Random House, 1980, p. 400.
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

A060409 gives associated "dropping times", A060410 the maximal values and A060411 the steps at which the maxima occur.
Cf. A006885, A006877, A006878, A033492, A060412-A060415, A132348.

Programs

  • Haskell
    a006884 n = a006884_list !! (n-1)
a006884_list = f 1 0 a025586_list where
   f i r (x:xs) = if x > r then i : f (i + 1) x xs else f (i + 1) r xs
-- Reinhard Zumkeller, May 11 2013
  • Mathematica
    mcoll[n_]:=Max@@NestWhileList[If[EvenQ[#],#/2,3#+1]&,n,#>1&]; t={1,max=2}; Do[If[(y=mcoll[n])>max,max=y; AppendTo[t,n]],{n,3,705000,4}]; t (* Jayanta Basu, May 28 2013 *)
DeleteDuplicates[Parallelize[Table[{n,Max[NestWhileList[If[EvenQ[#],#/2,3#+1]&,n,#>1&]]},{n,57*10^5}]],GreaterEqual[#1[[2]],#2[[2]]]&][[;;,1]] (* Harvey P. Dale, Apr 23 2023 *)
  • PARI
    A025586(n)=my(r=n); while(n>2, if(n%2, n=3*n+1; if(n>r, r=n)); n>>=1); r
r=0; for(n=1,1e6, t=A025586(n); if(t>r, r=t; print1(n", "))) \\ Charles R Greathouse IV, May 25 2016

A060409 In the '3x+1' problem, take the sequence of starting values which set new records for the highest point of the trajectory before reaching 1 (A006884); sequence gives associated "dropping time", number of steps to reach a lower value than the start.

Original entry on oeis.org

1, 4, 7, 7, 59, 13, 40, 23, 81, 61, 70, 65, 54, 72, 65, 59, 127, 105, 110, 59, 72, 164, 140, 73, 170, 105, 149, 97, 135, 183, 99, 99, 124, 156, 200, 140, 222, 264, 181, 243, 203, 238, 262, 362, 249, 183, 238, 226, 243, 294, 375, 455, 292, 245, 414
Offset: 1

Views

Author

N. J. A. Sloane, Apr 06 2001; b-file added Nov 27 2007

Keywords

Links

Crossrefs

Cf. A006884, A060410, A060411.

A060411 In the '3x+1' problem, take the sequence of starting values which set new records for the highest point of the trajectory before reaching 1 (A006884); sequence gives iterate where maximal value is reached in the trajectory with that start.

Original entry on oeis.org

0, 2, 3, 4, 45, 8, 31, 14, 48, 28, 49, 33, 26, 50, 35, 43, 67, 39, 69, 39, 35, 124, 83, 37, 132, 46, 81, 75, 83, 118, 68, 42, 72, 97, 98, 75, 92, 199, 109, 92, 92, 160, 91, 197, 119, 113, 109, 124, 176, 217, 234, 276, 172, 164, 233, 101, 109, 158, 157
Offset: 1

Views

Author

N. J. A. Sloane, Apr 06 2001; b-file added Nov 27 2007

Keywords

Links

Crossrefs

Cf. A006884, A060409, A060410.

A365483 In the Collatz (3x+1) problem, maximum excursion values corresponding to the starting points given by A365482.

Original entry on oeis.org

4616, 707118223359971240, 3562942561397226080, 103968231672274974522437732, 126114763591721667597212096, 1823036311464280263720932141024, 175294593968539094415936960141122, 32012333661096566765082938647132369010
Offset: 1

Views

Author

Paolo Xausa, Sep 05 2023

Keywords

Comments

See A365482 for corresponding maximum excursion ratios and additional information.

Links

Crossrefs

Subsequence of A060410.
Cf. A365478, A365482.

Formula

a(n) = A365478(A365482(n)).
Showing 1-6 of 6 results.

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

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