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 1-5 of 5 results.

A066145 In base 2, records for the number of 'Reverse and Add' steps needed to reach a palindrome.

Original entry on oeis.org

0, 1, 2, 4, 5, 11, 21, 32, 37, 46, 48, 49, 53, 89, 99, 142, 147, 273, 297, 345, 515, 550, 573
Offset: 1

Views

Author

Klaus Brockhaus, Dec 08 2001

Keywords

Comments

The analog of A065199 in base 2. A066144 gives the corresponding starting points.
Terms a(19..22) obtained by assuming that a(n+1) <= a(n) + 300. - A.H.M. Smeets, Apr 30 2022

Examples

			Starting with 74, 11 'Reverse and Add' steps are needed to reach a palindrome; starting with n < 74, at most 5 steps are needed.

Links

Crossrefs

Record values in base b: A077407 (b=3), A075687 (b=4), A306600 (b=8), A065199 (b=10), A348572 (Zeckendorf).
Cf. A062130, A066057, A066058, A066059, A066144.

Programs

  • Mathematica
    limit = 10^3; (* Assumes that there is no palindrome if none is found before "limit" iterations *)
best = -1; lst = {};
For[n = 0, n <= 10000, n++,
np = n; i = 0;
While[np != IntegerReverse[np, 2] && i < limit,
  np = np + IntegerReverse[np, 2]; i++];
If[i < limit && i > best, best = i; AppendTo[lst, i]]]; lst (* Robert Price, Oct 14 2019 *)

Extensions

Offset corrected and a(19)-a(23) by A.H.M. Smeets, Apr 30 2022

A075686 In base 4, n sets a new record for the number of Reverse and Add! steps needed to reach a palindrome starting with n.

Original entry on oeis.org

0, 4, 7, 26, 28, 127, 199, 296, 511, 3119, 16861, 18164, 19453, 20468, 270824
Offset: 0

Views

Author

Klaus Brockhaus, Sep 24 2002

Keywords

Comments

RECORDS transform of A075685. - Base-4 analog of A065198 (base 10) and A066144 (base 2). Integers like 290, for which a palindrome is (presumably) never reached (cf. A075420), are of course disregarded. A075687 gives the corresponding records.

Examples

			Starting with 26, 3 Reverse and Add! steps are needed to reach a palindrome; starting with n < 26, less (at most 2) steps are needed.

Links

Crossrefs

Cf. A065198, A066144, A075420, A075685, A075687.

A077406 In base 3: n sets a new record for the number of Reverse and Add! steps needed to reach a palindrome starting with n.

Original entry on oeis.org

0, 3, 5, 15, 17, 53, 1466, 9717, 32857, 37340, 37366, 37367, 531773, 1596329
Offset: 1

Views

Author

Klaus Brockhaus, Nov 05 2002

Keywords

Comments

RECORDS transform of A077402. - Base-3 analog of A066144 (base 2), A075686 (base 4) and A065198 (base 10). Integers like 103, for which a palindrome is (presumably) never reached (cf. A077404), are of course disregarded. A077407 gives the corresponding records.

Examples

			Starting with 15, 3 Reverse and Add! steps are needed to reach a palindrome; starting with n < 15, less (at most 2) steps are needed.

Links

Crossrefs

Cf. A065198, A066144, A075686, A077402, A077404, A077407.

Extensions

a(14) from Sean A. Irvine, Apr 19 2010

A306481 Lychrel numbers k that set a new record for the number of 'Reverse and Add' steps in base 2 needed to reach a Lychrel number m < k (i.e., its seed).

Original entry on oeis.org

22, 26, 67, 106, 157, 199, 281, 1145, 1594, 1798, 4326, 12794, 17407, 18428, 67583, 69628, 73978
Offset: 1

Views

Author

A.H.M. Smeets, Feb 18 2019

Keywords

Comments

Records in A306482.
Similar to the number of steps needed to reach a palindrome in the Reverse and Add! trajectories (see A066144 and A066145), the number of steps needed for a Lychrel number to reach the trajectory of its seed is relatively small.
Lychrel numbers in A066059; seeds in A075252 (for base 2).
As a clarification, this sequence can also be described as: Base 2 Lychrel numbers (A066059) k that sets a new record for the number of 'Reverse and Add' steps in base 2 needed to reach the trajectory of a base 2 Lychrel number seed (A075252) that is less than k. - Robert Price, Nov 20 2019

Crossrefs

Cf. A066059, A066144, A066145, A075252, A306482.

Programs

  • Mathematica
    limit = 200; (* Assumes that there is no palindrome if none is found before "limit" iterations *)
A066059 = Select[Range[50000],
   Length@NestWhileList[# + IntegerReverse[#, 2] &, #, # !=
         IntegerReverse[#, 2] &, 1, limit] == limit + 1 &];
utraj = {};
A075252 = Select[Range[50000],
   (x = NestWhileList[# + IntegerReverse[#, 2] &, #, # !=
         IntegerReverse[#, 2] & , 1, limit];
     If[Length@x >= limit  && Intersection[x, utraj] == {},
      utraj = Union[utraj, x]; True,
      utraj = Union[utraj, x]]) &];
A306481 = {}; best = -1; lastj = 0;
utraj = {};
For[i = 1, i <= Length@A066059, i++,
For[j = lastj + 1, j <= Length@A075252, j++,
  If[A066059[[i]] < A075252[[j]], Break[]];
  utraj = Union[utraj, NestList[# + IntegerReverse[#, 2] &, A075252[[j]], limit]];
  lastj = j; ];
l = NestWhileList[# + IntegerReverse[#, 2] &,
   A066059[[i]], ! MemberQ[utraj, #] &, 1, limit];
If[Length@l == limit + 1, Continue[]];
If[Length@l > best, best = Length@l; AppendTo[A306481, A066059[[i]]]];
]; A306481 (* Robert Price, Nov 20 2019 *)

A306482 Records for the number of 'Reverse and Add' steps in base 2 needed for a Lychrel number to join the trajectory of a smaller Lychrel number (i.e., its seed). Record setting numbers in A306481.

Original entry on oeis.org

0, 4, 5, 6, 9, 11, 17, 21, 22, 34, 52, 68, 83, 84, 91, 92, 98
Offset: 1

Views

Author

A.H.M. Smeets, Feb 18 2019

Keywords

Comments

Record setting numbers in A306481.
Similar to the number of steps needed to reach a palindrome in the Reverse and Add! trajectories (see A066144 and A066145), the number of steps needed for a Lychrel number to reach the trajectory of its seed is relatively small.
Lychrel numbers in A066059; seeds in A075252 (for base 2).
As a clarification, this sequence can also be described as: "Records for the number of 'Reverse and Add' steps in base 2 needed for a base 2 Lychrel number (A066059) to join the trajectory of a smaller base 2 Lychrel number seed (A075252)." - Robert Price, Nov 20 2019

Crossrefs

Cf. A066059, A066144, A066145, A075252, A306481.

Programs

  • Mathematica
    limit = 200; (* Assumes that there is no palindrome if none is found before "limit" iterations *)
A066059 = Select[Range[50000],
   Length@NestWhileList[# + IntegerReverse[#, 2] &, #, # !=
         IntegerReverse[#, 2] &, 1, limit] == limit + 1 &];utraj = {};
A075252 = Select[Range[50000],    (x = NestWhileList[# + IntegerReverse[#, 2] &, #, # !=
         IntegerReverse[#, 2] & , 1, limit];
     If[Length@x >= limit  && Intersection[x, utraj] == {},
      utraj = Union[utraj, x]; True,
      utraj = Union[utraj, x]]) &];A306482 = {}; best = -1; lastj = 0;
utraj = {};
For[i = 1, i <= Length@A066059, i++,
 For[j = lastj + 1, j <= Length@A075252, j++,
  If[A066059[[i]] < A075252[[j]], Break[]];
  utraj = Union[utraj, NestList[# + IntegerReverse[#, 2] &, A075252[[j]], limit]];
  lastj = j; ];
 l = NestWhileList[# + IntegerReverse[#, 2] &,
   A066059[[i]], ! MemberQ[utraj, #] &, 1, limit];
 If[Length@l == limit + 1, Continue[]];
If[Length@l > best, best = Length@l; AppendTo[A306482, Length@l - 1]]; ]; A306482  (* Robert Price, Nov 20 2019 *)
Showing 1-5 of 5 results.

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