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 1-10 of 18 results. Next

A072216 Consider the Reverse and Add! problem (cf. A001127); of all the n-digit numbers N which eventually reach a palindrome, pick that number N which takes the greatest number of steps to converge (in case of a tie, pick the smallest N); sequence gives values of N.

Original entry on oeis.org

5, 89, 187, 1297, 10911, 150296, 9008299, 15002893, 140669390, 1005499526, 10087799570
Offset: 1

Views

Author

N. J. A. Sloane, Jul 05 2002

Keywords

Comments

Since we do not even know if 196 eventually converges (see A006960, A023108) for n >= 3 these values are only conjectures.

Links

Crossrefs

Cf. A072217, A072218, A001127, A006960, A023108.

Extensions

Corrected and extended by Jason Doucette, May 20 2003; Oct 09 2005

A072217 Consider the Reverse and Add! problem (cf. A001127); of all the n-digit numbers N which eventually reach a palindrome, pick that number N which takes the greatest number of steps to converge (in case of a tie, pick the smallest N); sequence gives number of steps N takes to converge.

Original entry on oeis.org

2, 24, 23, 21, 55, 64, 96, 96, 98, 109, 149, 149, 188, 186, 201, 197, 236, 232
Offset: 1

Views

Author

N. J. A. Sloane, Jul 05 2002

Keywords

Comments

Since we do not even know if 196 eventually converges (see A006960, A023108) for n >= 3 these values are only conjectures.

Links

Crossrefs

Cf. A072216, A072218, A001127, A006960, A023108.

Extensions

Corrected and extended by Jason Doucette, Mar 29 2005; Oct 09 2005

A072218 Consider the Reverse and Add! problem (cf. A001127); of all the n-digit numbers N which eventually reach a palindrome, pick that number N which takes the greatest number of steps to converge (in case of a tie, pick the smallest N); sequence gives palindrome that is reached.

Original entry on oeis.org

11, 8813200023188, 8813200023188, 8813200023188, 4668731596684224866951378664, 682049569465550121055564965940286, 555458774083726674580862268085476627380477854555, 555458774083726674580862268085476627380477854555, 1345428953367763125675365555635765213677633598245431
Offset: 1

Views

Author

N. J. A. Sloane, Jul 05 2002

Keywords

Comments

Since we do not even know if 196 eventually converges (see A006960, A023108) for n >= 3 these values are only conjectures.

Links

Crossrefs

Cf. A072216, A072217, A001127, A006960, A023108.

A145733 Indices of palindromes in A001127.

Original entry on oeis.org

1, 2, 3, 4, 6, 9, 10, 11, 12, 16, 18
Offset: 1

Views

Author

Dmitry Kamenetsky, Oct 17 2008

Keywords

Comments

The next term (if it exists) is greater than 10000.
These are actually indices into A001127 right-shifted; A001127 has offset 0, but this sequence treats it as having offset 1.

Examples

			The 9th term in A001127 is 1111, which is a palindrome, thus 9 is in the sequence.

Crossrefs

A001127

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 *)

A033651 Trajectory of 9 under map x->x + (x-with-digits-reversed).

Original entry on oeis.org

9, 18, 99, 198, 1089, 10890, 20691, 40293, 79497, 158994, 658845, 1207701, 2284722, 4559544, 9019098, 17928207, 88211178, 175322466, 839546037, 1570191975, 7362102726, 13634115363, 49985258994, 99970517988, 188942025987, 978462275868, 1847034540747, 9317488848228
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

Trajectories of 27, 36, 45, 54, 63, 72, 81, 90, ..., merge into this sequence. - Robert G. Wilson v, Dec 16 2005.

Links

Crossrefs

Cf. A006960, A001127, A033648, A033649, A033650.
Cf. A056964, A004086.
Row n=9 of A243238.
Partial sums of A112296.

Programs

  • Haskell
    a063051 n = a063051_list !! n
a063051_list = iterate a056964 879 -- Reinhard Zumkeller, Sep 22 2011
  • Maple
    a:= proc(n) option remember; `if`(n=0, 9, (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@# &, 9, 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 *)

A374734 a(n) = a(n-1) + rotate(a(n-1), n-1 digits left) with a(1) = 1.

Original entry on oeis.org

1, 2, 4, 8, 16, 77, 154, 695, 1264, 3905, 4444, 8888, 17776, 93953, 133348, 481481, 1296295, 7591424, 11839015, 50854133, 92189218, 114081407, 928152547, 1182945362, 10636566544, 47203110650, 78309615370, 139846693679, 606783485077, 955291245755, 1201047201046
Offset: 1

Views

Author

Nicholas M. R. Frieler, Jul 17 2024

Keywords

Examples

			Here we use -m (where m > 0) to represent rotating the digits of a number m digits to the left.
a(9) = a(8) + rotate(a(8), -8) = 695 + rotate(695, -8) = 695 + 569 = 1264.

Links

Crossrefs

Cf. A001127, A051300, A051299, A374731, A374732, A374733.

Programs

  • Mathematica
    a[1] = 1; a[n_] := a[n] = a[n - 1] + FromDigits@RotateLeft[IntegerDigits[a[n - 1]], n - 1]; arr = a[#] & /@ Range[1, 100]
nxt[{n_,a_}]:={n+1,a+FromDigits[RotateLeft[IntegerDigits[a],n]]}; NestList[nxt,{1,1},30][[;;,2]] (* Harvey P. Dale, Nov 08 2024 *)
Showing 1-10 of 18 results. Next

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

Content is available under The OEIS End-User License Agreement.