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 1-7 of 7 results.

A001127 Trajectory of 1 under map x->x + (x-with-digits-reversed).

Original entry on oeis.org

1, 2, 4, 8, 16, 77, 154, 605, 1111, 2222, 4444, 8888, 17776, 85547, 160105, 661166, 1322332, 3654563, 7309126, 13528163, 49710694, 99312488, 187733887, 976071668, 1842242347, 9274664828, 17559329557, 93151725128, 175304440267, 937348843838, 1775697687577
Offset: 0

Views

Author

N. J. A. Sloane, Jun 05 2002

Keywords

Comments

Normally one stops as soon as a palindrome is reached.
A Reverse and Add! sequence.
Trajectories of 25, 34, 43, 52, 59, 61, 68, 70, 86, 95, ..., merge into this sequence. - Robert G. Wilson v, Dec 16 2005

Links

Crossrefs

Cf. A006960, A023108, A033648, A033649, A033650, A033651.
Cf. A056964, A004086.
Row n=1 of A243238.

Programs

  • Haskell
    a001127 n = a001127_list !! n
a001127_list = iterate a056964 1 -- Reinhard Zumkeller, Sep 22 2011
  • Maple
    a:= proc(n) option remember; `if`(n=0, 1, (h-> h+ (s->
      parse(cat(s[-i]$i=1..length(s))))(""||h))(a(n-1)))
    end:
seq(a(n), n=0..40);  # Alois P. Heinz, Jun 18 2014
  • Mathematica
    NestList[ # + FromDigits@Reverse@IntegerDigits@# &, 1, 30] (* Robert G. Wilson v, Dec 16 2005 *)
NestList[#+IntegerReverse[#]&,1,30] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Nov 19 2019 *)

A033648 Trajectory of 3 under map x->x + (x-with-digits-reversed).

Original entry on oeis.org

3, 6, 12, 33, 66, 132, 363, 726, 1353, 4884, 9768, 18447, 92928, 175857, 934428, 1758867, 9447438, 17794887, 96644658, 182289327, 906271608, 1712444217, 8836886388, 17673772776, 85401510447, 159803020905, 668823329856, 1327746658722, 3606313135953, 7201626272016
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

Normally one stops as soon as a palindrome is reached.
A Reverse and Add! sequence.

Links

Crossrefs

Cf. A006960, A001127, A033649, A033650, A033651.
Cf. A056964, A004086.
Row n=3 of A243238.

Programs

  • Haskell
    a033648 n = a033648_list !! n
a033648_list = iterate a056964 3 -- Reinhard Zumkeller, Sep 22 2011
  • Maple
    a:= proc(n) option remember; `if`(n=0, 3, (h-> h+ (s->
      parse(cat(s[-i]$i=1..length(s))))(""||h))(a(n-1)))
    end:
seq(a(n), n=0..40);  # Alois P. Heinz, Jun 18 2014
  • Mathematica
    NestList[ # + FromDigits@Reverse@IntegerDigits@# &, 3, 29] (* Robert G. Wilson v, Dec 16 2005 *)

A243238 Table T(n,r) of terms in the reverse and add sequences of positive integers n read by antidiagonals.

Original entry on oeis.org

1, 2, 2, 4, 4, 3, 8, 8, 6, 4, 16, 16, 12, 8, 5, 77, 77, 33, 16, 10, 6, 154, 154, 66, 77, 11, 12, 7, 605, 605, 132, 154, 22, 33, 14, 8, 1111, 1111, 363, 605, 44, 66, 55, 16, 9, 2222, 2222, 726, 1111, 88, 132, 110, 77, 18, 10, 4444, 4444, 1353, 2222, 176, 363, 121, 154, 99, 11, 11
Offset: 1

Views

Author

Felix Fröhlich, Jun 12 2014

Keywords

Examples

			T(5,6) = 88, since 88 is the 6th term in the reverse and add sequence of 5.
Table starts with:
  1 2 4 8 16 77 154 605 1111 2222
  2 4 8 16 77 154 605 1111 2222 4444
  3 6 12 33 66 132 363 726 1353 4884
  4 8 16 77 154 605 1111 2222 4444 8888
  5 10 11 22 44 88 176 847 1595 7546
  6 12 33 66 132 363 726 1353 4884 9768
  7 14 55 110 121 242 484 968 1837 9218
  8 16 77 154 605 1111 2222 4444 8888 17776
  9 18 99 198 1089 10890 20691 40293 79497 158994
  10 11 22 44 88 176 847 1595 7546 14003

Links

Crossrefs

Rows n=1, 3, 5, 7, 9 give: A001127, A033648, A033649, A033650, A033651.
Cf. A006960, A023108, A033670, A088753, A089694, A240510.
Main diagonal gives A244058.

Programs

  • Maple
    T:= proc(n, r) option remember; `if`(r=1, n, (h-> h +(s->
      parse(cat(s[-i]$i=1..length(s))))(""||h))(T(n, r-1)))
    end:
seq(seq(T(n, 1+d-n), n=1..d), d=1..12);  # Alois P. Heinz, Jun 18 2014
  • Mathematica
    rad[n_] := n + FromDigits[Reverse[IntegerDigits[n]]];
T[n_, 1] := n; T[n_, k_] := T[n, k] = rad[T[n, k-1]];
Table[T[n-k+1, k], {n, 1, 12}, {k, n, 1, -1}] // Flatten (* Jean-François Alcover, Apr 08 2016 *)

A033650 Trajectory of 7 under map x --> x + (x-with-digits-reversed).

Original entry on oeis.org

7, 14, 55, 110, 121, 242, 484, 968, 1837, 9218, 17347, 91718, 173437, 907808, 1716517, 8872688, 17735476, 85189247, 159487405, 664272356, 1317544822, 3602001953, 7193004016, 13297007933, 47267087164, 93445163438, 176881317877, 955594506548, 1801200002107
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

A Reverse and Add! sequence.
Trajectories of 19, 23, 28, 29, 32, 37, 38, 41, 46, 47, 49, 50, ..., merge into this sequence. - Robert G. Wilson v, Dec 16 2005
A Reverse and Add! sequence.

Links

Crossrefs

Cf. A006960, A001127, A033648, A033649, A033651.
Cf. A056964, A004086.
Row n=7 of A243238.

Programs

  • Haskell
    a033650 n = a033650_list !! n
a033650_list = iterate a056964 7 -- Reinhard Zumkeller, Sep 22 2011
  • Maple
    a:= proc(n) option remember; `if`(n=0, 7, (h-> h+ (s->
      parse(cat(s[-i]$i=1..length(s))))(""||h))(a(n-1)))
    end:
seq(a(n), n=0..40);  # Alois P. Heinz, Jun 18 2014
  • Mathematica
    NestList[ # + FromDigits@Reverse@IntegerDigits@# &, 7, 26] (* Robert G. Wilson v *)

A033649 Trajectory of 5 under map x->x + (x-with-digits-reversed).

Original entry on oeis.org

5, 10, 11, 22, 44, 88, 176, 847, 1595, 7546, 14003, 44044, 88088, 176176, 847847, 1596595, 7553546, 14007103, 44177144, 88354288, 176599676, 853595347, 1597190705, 6668108656, 13236127322, 35608290553
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

Trajectories of 15, 21, 24, 30, 39, 42, 48, 51, 57, 60, 69, 75, 78, 84, 87, 93, 96, ..., merge into this sequence. - Robert G. Wilson v, Dec 16 2005
A Reverse and Add! sequence.
Trajectories of 13, 17, 20, 26, 31, 35, 40, 53, 62, 71, 79, 80, 97, ..., merge into this sequence. - Robert G. Wilson v, Dec 16 2005

Links

Crossrefs

Cf. A006960, A001127, A033648, A033650, A033651.
Cf. A056964, A004086.
Row n=5 of A243238.

Programs

  • Haskell
    a033649 n = a033649_list !! n
a033649_list = iterate a056964 5 -- Reinhard Zumkeller, Sep 22 2011
  • Maple
    a:= proc(n) option remember; `if`(n=0, 5, (h-> h+ (s->
      parse(cat(s[-i]$i=1..length(s))))(""||h))(a(n-1)))
    end:
seq(a(n), n=0..40);  # Alois P. Heinz, Jun 18 2014
  • Mathematica
    NestList[ # + FromDigits@Reverse@IntegerDigits@# &, 5, 29] (* Robert G. Wilson v, Dec 16 2005 *)

A063051 'Reverse and Add!' trajectory of 879.

Original entry on oeis.org

879, 1857, 9438, 17787, 96558, 182127, 903408, 1707717, 8884788, 17759676, 85455447, 159910905, 668930856, 1326970722, 3597766953, 7194444906, 13288889823, 46187778054, 91275556218, 172541113437, 906852258708
Offset: 0

Views

Author

Klaus Brockhaus, Jul 07 2001

Keywords

Examples

			a(1) = 879 + 978 = 1857.

Links

Crossrefs

Cf. A033865, A023108, A006960, A063052, A056964, A004086.

Programs

  • ARIBAS
    m := 879; stop := 25; c := 0; rev := int_reverse(m); while m <> rev and c < stop do inc(c); write(m," "); m := m + rev; rev := int_reverse(m); end;
  • Haskell
    a033651 n = a033651_list !! n
a033651_list = iterate a056964 9 -- Reinhard Zumkeller, Sep 22 2011
  • Mathematica
    NestList[# + FromDigits[Reverse[IntegerDigits[#]]]&, 879, 40] (* Vincenzo Librandi, Sep 23 2013 *)
  • PARI
    Rev(x)= { local(d); r=0; while (x>0, d=x-10*(x\10); x\=10; r=r*10 + d); return(r) }
{ for (n=0, 200, if (n, a+=Rev(a), a=879); write("b063051.txt", n, " ", a) ) } \\ Harry J. Smith, Aug 16 2009

A033659 Trajectory of 27 under map x->x + (x-with-digits-reversed).

Original entry on oeis.org

27, 99, 198, 1089, 10890, 20691, 40293, 79497, 158994, 658845, 1207701, 2284722, 4559544, 9019098, 17928207, 88211178, 175322466, 839546037, 1570191975, 7362102726, 13634115363, 49985258994, 99970517988
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Essentially the same as A033651.
Showing 1-7 of 7 results.

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

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