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.

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A063064 Integers n > 10563 such that the 'Reverse and Add!' trajectory of n joins the trajectory of 10563.

Original entry on oeis.org

11553, 12543, 13533, 14097, 14523, 15087, 15513, 16077, 16503, 17067, 18057, 18597, 19047, 19587, 20562, 21552, 22542, 24096, 24522, 25086, 25512, 26076, 26502, 27066, 28056, 28596, 29046, 29586, 30561, 31551, 32541, 33531, 34095
Offset: 0

Views

Author

Klaus Brockhaus, Jul 07 2001

Keywords

Comments

Subsequence of A023108.

Examples

			The trajectory of 12543 reaches 47064 in one step and 47064 is a term in the trajectory of 10563, so 12543 belongs to the present sequence. The corresponding term in A063065, giving the number of steps, accordingly is 1.

Links

Crossrefs

A033865, A023108, A063063, A063065.

A063065 a(n) = number of 'Reverse and Add!' operations that have to be applied to the n-th term of A063064 in order to obtain a term in the trajectory of 10563.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 3, 1, 3, 1, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 3, 1, 2, 3, 1, 1, 1, 0
Offset: 0

Views

Author

Klaus Brockhaus, Jul 07 2001

Keywords

Examples

			12543 is a term of A063064. One 'Reverse and Add!' operation applied to 12543 leads to a term (47064) in the trajectory of 10563, so the corresponding term of the present sequence is 1.

Links

Crossrefs

A023108, A033865, A063063, A063064.

A063434 Integers k > 10577 such that the 'Reverse and Add!' trajectory of k joins the trajectory of 10577.

Original entry on oeis.org

11567, 12557, 13547, 14537, 15527, 16517, 17507, 20576, 21566, 22556, 23546, 24536, 25526, 26516, 27506, 30575, 31565, 32555, 33545, 34535, 35525, 36515, 37505, 40574, 41564, 42554, 43544, 44534, 45524, 46514, 47504, 50573, 51563
Offset: 0

Views

Author

Klaus Brockhaus, Jul 20 2001

Keywords

Comments

Subsequence of A023108.
The first term not congruent 83 mod 99 is a(47) = 70069, thereafter the residues show no obvious pattern. - Klaus Brockhaus, Jul 14 2003

Examples

			The trajectory of 12557 reaches 88078 in one step and 88078 is a term in the trajectory of 10577, so 12557 belongs to the present sequence. The corresponding term in A063435, giving the number of steps, accordingly is 1.

Links

Crossrefs

Cf. A033865, A023108, A063433, A063435.

A066055 Integers n > 10583 such that the 'Reverse and Add!' trajectory of n joins the trajectory of 10583.

Original entry on oeis.org

11573, 12563, 13553, 13597, 14543, 14587, 15533, 15577, 16523, 16567, 17513, 17557, 18097, 18503, 18547, 19087, 19537, 20582, 21572, 22562, 23552, 23596, 24586, 25532, 25576, 26522, 26566, 27512, 27556, 28096, 28502, 28546, 29086
Offset: 0

Views

Author

Klaus Brockhaus, Nov 30 2001

Keywords

Comments

Subsequence of A023108.

Examples

			The trajectory of 13597 reaches 937838 in three steps and 937838 is a term in the trajectory of 10583, so 13597 belongs to the present sequence. The corresponding term in A066056, giving the number of steps, accordingly is 3.

Links

Crossrefs

Cf. A033865, A023108, A066054, A066056.

A072139 Last term of the preperiodic part of the 'Reverse and Subtract' trajectory of n, or -1 if the trajectory is completely periodic.

Original entry on oeis.org

-1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 9, 11, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 22, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 33, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 44, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 55, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 66, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 77, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 88, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 99, 99, 101, 99
Offset: 0

Views

Author

Klaus Brockhaus, Jun 24 2002

Keywords

Comments

'Reverse and Subtract' (cf. A072137) is defined by x -> |x - reverse(x)|. For small n the positive terms are the first palindrome in the trajectory of n, so this sequence is a weak analog of A033865, which uses 'Reverse and Add'. a(1012) = 8712 is the first non-palindrome (cf. A072140). For k in A072140, A072141 or A072142 we have a(k) = -1.

Examples

			a(0) = -1, since 0 -> |0 - 0| = 0, the preperiodic part is empty; a(12) = 9, since 12 -> |12 - 21| = 9.

Crossrefs

Cf. A033865, A072137, A072140, A072141, A072142.

A063050 a(n) = number of 'Reverse and Add!' operations that have to be applied to the n-th term of A063049 in order to obtain a term in the trajectory of 196.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 0, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1
Offset: 0

Views

Author

Klaus Brockhaus, Jul 07 2001

Keywords

Examples

			394 is a term of A063049. One 'Reverse and Add!' operation applied to 394 leads to a term (887) in the trajectory of 196, so the corresponding term of the present sequence is 1.

Links

Crossrefs

A023108, A033865, A006960, A063049.

Programs

  • Mathematica
    limit = 10^3; x = NestList[ # + IntegerReverse[#] &, 196, limit];
y = Select[Range[197, 4942],
   Intersection[NestList[ # + IntegerReverse[#] &, #, limit],
      x] != {} &];
Table[
 Length@NestWhileList[# + IntegerReverse[#] &,
    y[[i]], ! MemberQ[x, #] &] - 1, {i, Length[y]}]
(* Robert Price, Oct 21 2019 *)

A063053 a(n) = number of 'Reverse and Add!' operations that have to be applied to the n-th term of A063052 in order to obtain a term in the trajectory of 879.

Original entry on oeis.org

1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 0, 1, 1, 1, 2, 2, 2, 4, 5, 4, 3, 4, 5, 3, 4, 3, 4, 3, 4, 3, 1, 3, 0, 3, 1, 3, 1, 4, 5, 4, 5, 3, 4, 5, 3, 4, 3, 4, 3, 4, 3
Offset: 0

Views

Author

Klaus Brockhaus, Jul 07 2001

Keywords

Examples

			1497 is a term of A063052. One 'Reverse and Add!' operation applied to 1497 leads to a term (9438) in the trajectory of 879, so the corresponding term of the present sequence is 1.

Links

Crossrefs

A023108, A033865, A063051, A063052.

A063056 a(n) = number of 'Reverse and Add!' operations that have to be applied to the n-th term of A063055 in order to obtain a term in the trajectory of 1997.

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 0, 3, 3, 3, 3, 3, 1, 3, 0, 3, 1, 3, 3, 3, 3, 3, 1, 3, 1, 3, 1, 3, 3, 3, 3, 3, 1, 3, 1, 3, 1, 3, 3, 3, 3, 1, 3, 3, 1, 3, 3, 3, 3, 3, 1, 3, 1, 3, 1, 3, 3, 3, 3, 3, 1, 3, 1, 3, 1, 3, 3, 3, 3, 3, 1, 3, 1, 3, 1, 2, 2, 2, 3, 2, 3, 2, 1, 3
Offset: 0

Views

Author

Klaus Brockhaus, Jul 07 2001

Keywords

Examples

			3995 is a term of A063055. One 'Reverse and Add!' operation applied to 3995 leads to a term (9988) in the trajectory of 1997, so the corresponding term of the present sequence is 1.

Links

Crossrefs

A023108, A033865, A063054, A063055.

A063059 a(n) = number of 'Reverse and Add!' operations that have to be applied to the n-th term of A063058 in order to obtain a term in the trajectory of 7059.

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 1, 1, 1, 0, 2, 1, 3, 2, 1, 3, 2, 1, 1, 1, 1, 1, 2, 1, 3, 2, 1, 3, 2, 1, 1, 1, 1, 1, 2, 1, 3, 2, 1, 3, 2, 1, 1, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 3, 2, 1, 3, 2, 1
Offset: 0

Views

Author

Klaus Brockhaus, Jul 07 2001

Keywords

Examples

			7239 is a term of A063058. One 'Reverse and Add!' operation applied to 7239 leads to a term (16566) in the trajectory of 7059, so the corresponding term of the present sequence is 1.

Links

Crossrefs

A023108, A033865, A063057, A063058.

A063062 a(n) = number of 'Reverse and Add!' operations that have to be applied to the n-th term of A063061 in order to obtain a term in the trajectory of 10553.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 3, 1, 3, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 3, 1, 3, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 3, 1, 3, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 1, 3, 1, 3, 1, 3, 1, 1, 1, 1, 1, 3, 1, 3, 1, 3, 1, 3, 1, 1, 1, 1, 1, 3, 1, 3, 1, 3, 1, 3, 1, 1, 1, 1, 1, 3, 1, 3, 1, 3
Offset: 0

Views

Author

Klaus Brockhaus, Jul 07 2001

Keywords

Examples

			12097 is a term of A063061. One 'Reverse and Add!' operation applied to 12097 leads to a term (91118) in the trajectory of 10553, so the corresponding term of the present sequence is 1.

Links

Crossrefs

A023108, A033865, A063060, A063061.
Previous Showing 31-40 of 42 results. Next

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

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