A001127 -id:A001127 - cp's OEIS frontend

A244567 Triangle T(n,k) in which the n-th row lists in increasing order all values s such that n is in the trajectory of the 'Reverse and Add!' sequence starting with s; triangle T(n,k), n>=0, 1<=k<=A244569(n), read by rows.

0, 1, 1, 2, 3, 1, 2, 4, 5, 3, 6, 7, 1, 2, 4, 8, 9, 5, 10, 5, 10, 11, 3, 6, 12, 13, 7, 14, 15, 1, 2, 4, 8, 16, 17, 9, 18, 19, 20, 21, 5, 10, 11, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 3, 6, 12, 21, 30, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43

Offset: 0

Alois P. Heinz, Jun 30 2014

			Triangle T(n,k) begins:
   0;
   1;
   1,  2;
   3;
   1,  2,  4;
   5;
   3,  6;
   7;
   1,  2,  4,  8;
   9;
   5, 10;
   5, 10, 11;
   3,  6, 12;
  13;
   7, 14;
  15;
   1,  2,  4,  8,  16;
  17;

Alois P. Heinz, Rows n = 0..6000, flattened

Column k=0 gives A244568.
Last elements of rows give A001477.
Cf. A001127, A033648, A033670, A006960, A004086, A244569.

A244568 Smallest value s such that n is in the trajectory of the 'Reverse and Add!' sequence starting with s.

Original entry on oeis.org

0, 1, 1, 3, 1, 5, 3, 7, 1, 9, 5, 5, 3, 13, 7, 15, 1, 17, 9, 19, 20, 21, 5, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 3, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 5, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 7, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 3, 67, 68, 69

Offset: 0

Alois P. Heinz, Jun 30 2014

Alois P. Heinz, Table of n, a(n) for n = 0..20000

Column k=0 of A244567.

Cf. A001127, A033648, A033670, A006960, A004086, A244569.

A244569 Number of values s such that n is in the trajectory of the 'Reverse and Add!' sequence starting with s.

Original entry on oeis.org

1, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 3, 3, 1, 2, 1, 5, 1, 2, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 12, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 12, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 17

Offset: 0

Alois P. Heinz, Jun 30 2014

Alois P. Heinz, Table of n, a(n) for n = 0..20000

Row lengths of A244567.

Cf. A001127, A033648, A033670, A006960, A004086, A244568.

A374731 a(n) = a(n-1) + rotate(a(n-1), n-2 digits right) with a(1) = 1.

Original entry on oeis.org

1, 2, 4, 8, 16, 32, 55, 110, 121, 332, 664, 1130, 2431, 4862, 7348, 12221, 24442, 46886, 133354, 266708, 1093378, 2027159, 4054318, 12459749, 37057240, 74114480, 81525928, 110341187, 220682374, 642750611, 759178117, 876937295, 1606524988, 10422590237, 20845180474, 62929698521, 84558995506

Offset: 1

Nicholas M. R. Frieler, Jul 17 2024

			a(12) = a(11) + rotate(a(11), 11) = 1130 + rotate(1130, 11) = 1130 + 1301 = 2431.

Cf. A001127, A051300, A051299, A374732, A374733, A374734.

a[1] = 1; a[n_] := a[n] = a[n - 1] + FromDigits@RotateRight[IntegerDigits[a[n - 1]], n - 2]; arr = a[#] & /@ Range[0, 100]

A374732 a(n) = a(n-1) + rotate(a(n-1), n-1 digits right) with a(1) = 1.

Original entry on oeis.org

1, 2, 4, 8, 16, 77, 154, 569, 1264, 5390, 14443, 45887, 133345, 646679, 1443145, 6587459, 12553333, 43808666, 110246752, 321271427, 594484141, 736078625, 1598652232, 3920250884, 4804642909, 9095590955, 15005150050, 65055300101, 95065465156, 149717034662

Offset: 1

Nicholas M. R. Frieler, Jul 17 2024

			a(12) = a(11) + rotate(a(11), 11) = 14443 + rotate(14443, 11) = 14443 + 31444 = 45887.

Cf. A001127, A051300, A051299, A374731, A374733, A374734.

a[1] = 1; a[n_] := a[n] = a[n - 1] + FromDigits@RotateRight[IntegerDigits[a[n - 1]], n - 1]; arr = a[#] & /@ Range[1, 100]

A374733 a(n) = a(n-1) + rotate(a(n-1), n-2 digits left) with a(1) = 1.

Original entry on oeis.org

1, 2, 4, 8, 16, 32, 55, 110, 211, 332, 664, 1310, 1441, 2882, 11704, 52874, 105748, 586805, 1145485, 5996630, 9056596, 15962255, 41478217, 58892999, 154782298, 452937080, 1257466450, 7707592196, 9675299788, 18572052785, 46423909990, 145470333899, 484461788602

Offset: 1

Nicholas M. R. Frieler, Jul 17 2024

			a(13) = a(12) + rotate_left(a(12), 11) = 1310 + rotate_left(1310, 11) = 1310 + 0131 = 1441.

Cf. A001127, A051300, A051299, A374731, A374732, A374734.

a[1] = 1; a[n_] := a[n] = a[n - 1] + FromDigits@RotateLeft[IntegerDigits[a[n - 1]], n - 2]; arr = a[#] & /@ Range[1, 100]

A244058 n-th term of the 'Reverse and Add!' sequence starting with n.

Original entry on oeis.org

1, 4, 12, 77, 44, 363, 484, 4444, 79497, 14003, 88088, 175857, 1596595, 1716517, 17794887, 13528163, 176599676, 839546037, 1317544822, 853595347, 8836886388, 13236127322, 13297007933, 668823329856, 175304440267, 909153350908, 9317488848228, 8813200023188

Offset: 1

Alois P. Heinz, Jun 18 2014

a(n) is a palindrome for n in {1, 2, 4, 5, 6, 7, 8, 9, 11, 21, 28, 30}.

Alois P. Heinz, Table of n, a(n) for n = 1..1000
Index entries for sequences related to Reverse and Add!

Main diagonal of A243238.

Cf. A001127, A033648, A033670, A006960, A004086.

b:= proc(n, j) option remember; `if`(j=1, n, (h-> h+ (s->
      parse(cat(s[-i]$i=1..length(s))))(""||h))(b(n, j-1)))
    end:
a:= n-> b(n$2):
seq(a(n), n=1..40);

Table[Nest[#+IntegerReverse[#]&,n,n-1],{n,30}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 07 2021 *)

A285741 a(0) = 1; a(2n) = a(n), a(2n+1) = a(n) + R(a(n)), where R() is the digit reversal.

Original entry on oeis.org

1, 2, 2, 4, 2, 4, 4, 8, 2, 4, 4, 8, 4, 8, 8, 16, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 77, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 77, 4, 8, 8, 16, 8, 16, 16, 77, 8, 16, 16, 77, 16, 77, 77, 154, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 77, 4, 8, 8, 16, 8, 16, 16, 77, 8, 16, 16

Offset: 0

Ilya Gutkovskiy, Apr 25 2017

			a(0) = 1;
a(1) = a(2*0+1) = a(0) + R(a(0)) = 1 + 1 = 2;
a(2) = a(2*1) = a(1) = 2;
a(3) = a(2*1+1) = a(1) + R(a(1)) = 2 + 2 = 4;
a(4) = a(2*2) = a(2) = 2;
a(5) = a(2*2+1) = a(2) + R(a(2)) = 2 + 2 = 4, etc.

Michael Gilleland, Some Self-Similar Integer Sequences
Index entries for sequences related to Reverse and Add!

Cf. A001127 (records), A004086, A056964.

a[0] = 0; a[n_] := If[EvenQ[n], a[n/2], a[(n - 1)/2] + FromDigits[Reverse[IntegerDigits[a[(n - 1)/2]]]] ]; Table[a[n], {n, 0, 90}]

cp's OEIS Frontend

A244567 Triangle T(n,k) in which the n-th row lists in increasing order all values s such that n is in the trajectory of the 'Reverse and Add!' sequence starting with s; triangle T(n,k), n>=0, 1<=k<=A244569(n), read by rows.

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A244568 Smallest value s such that n is in the trajectory of the 'Reverse and Add!' sequence starting with s.

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A244569 Number of values s such that n is in the trajectory of the 'Reverse and Add!' sequence starting with s.

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A374731 a(n) = a(n-1) + rotate(a(n-1), n-2 digits right) with a(1) = 1.

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Mathematica

A374732 a(n) = a(n-1) + rotate(a(n-1), n-1 digits right) with a(1) = 1.

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Mathematica

A374733 a(n) = a(n-1) + rotate(a(n-1), n-2 digits left) with a(1) = 1.

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Mathematica

A244058 n-th term of the 'Reverse and Add!' sequence starting with n.

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Mathematica

A285741 a(0) = 1; a(2*n) = a(n), a(2*n+1) = a(n) + R(a(n)), where R() is the digit reversal.

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Mathematica

A285741 a(0) = 1; a(2n) = a(n), a(2n+1) = a(n) + R(a(n)), where R() is the digit reversal.