A117831 -id:A117831 - cp's OEIS frontend

A118473 Records in A117831.

1, 40, 43, 47, 50, 53, 2636, 2639, 2640, 2643, 2644, 2730, 2739, 3008, 251505, 251995, 252485, 252975, 253465, 253506, 253510, 253513, 253514, 253515, 253516, 253517, 253520, 253521, 253522, 255008, 25037505, 25087495, 25137485, 25187475

Offset: 1

N. J. A. Sloane, May 05 2006

Klaus Brockhaus, Table of n, a(n) for n = 1,...,45
N. J. A. Sloane and others, Sequences of RADD type, OEIS wiki.

Cf. A117831, A118474.

a(8)-a(13) from N. J. A. Sloane, May 06 2006
a(14)-a(20) from Klaus Brockhaus, May 07 2006
a(21)-a(34) from Klaus Brockhaus, Aug 01 2006

A118474 Where records occur in A117831.

Original entry on oeis.org

1, 3, 18, 29, 44, 104, 111, 297, 392, 479, 574, 1013, 1994, 10013, 10115, 10135, 10155, 10175, 10195, 11021, 30013, 49999, 59994, 100022, 199018, 239991, 389928, 429983, 979924, 1000013, 1001015, 1001035, 1001055, 1001075, 1001095, 1001195, 1001295

Offset: 1

N. J. A. Sloane, May 05 2006

a(1) to a(13) enter the only cycle of length 54 (cf. A117830), a(14) to a(29) enter a cycle of length 90 (cf. A117807), a(30) to a(45) enter a cycle of length 1890.

Klaus Brockhaus, Table of n, a(n) for n = 1..45
N. J. A. Sloane and others, Sequences of RADD type, OEIS wiki.

Cf. A117831, A118473.

a(8)-a(13) from N. J. A. Sloane, May 06 2006
a(14)-a(20) from Klaus Brockhaus, May 07 2006
a(21)-a(37) from Klaus Brockhaus, Aug 01 2006

A117521 Start with 1 and repeatedly reverse the digits and add 2 to get the next term.

Original entry on oeis.org

1, 3, 5, 7, 9, 11, 13, 33, 35, 55, 57, 77, 79, 99, 101, 103, 303, 305, 505, 507, 707, 709, 909, 911, 121, 123, 323, 325, 525, 527, 727, 729, 929, 931, 141, 143, 343, 345, 545, 547, 747, 749, 949, 951, 161, 163, 363, 365, 565, 567, 767, 769, 969, 971, 181, 183, 383, 385, 585, 587, 787, 789, 989, 991, 201, 104, 403, 306, 605, 508, 807, 710, 19, 93, 41, 16, 63, 38, 85, 60, 8, 10, 3, 5, 7, 9, 11, 13, 33, 35, 55, 57, 77, 79, 99, 101, 103, 303, 305, 505, 507, 707

Offset: 1

N. J. A. Sloane, following discussions with Luc Stevens, May 04 2006

N. J. A. Sloane and others, Sequences of RADD type, OEIS wiki.
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

Cf. A117831, A118514.

After 1 step enters a cycle of length 81.

A118514 Define sequence S_n by: initial term = n, reverse digits and add 2 to get next term. It is conjectured that S_n always reaches a cycle. Sequence gives number of steps for S_n to reach a cycle.

Original entry on oeis.org

1, 3, 0, 2, 0, 1, 0, 0, 0, 0, 0, 9, 0, 7, 10, 0, 9, 4, 0, 3, 8, 8, 8, 7, 15, 5, 5, 3, 12, 1, 11, 16, 0, 7, 0, 5, 8, 0, 7, 2, 0, 6, 6, 6, 6, 5, 13, 3, 3, 1, 10, 6, 9, 14, 0, 5, 0, 3, 6, 0, 5, 4, 0, 4, 4, 4, 4, 3, 11, 1, 1, 13, 8, 4, 7, 12, 0, 3, 0, 1, 4, 2, 3, 2, 0, 2, 2, 2, 2, 1, 9, 12, 0

Offset: 1

N. J. A. Sloane, May 06 2006

Initial cycles have length 81 or 90.
There is one cycle of length 81 (least component is 3, all components have at most three digits, cf. A117521), 22 cycles of length 90 with 4-digit components (least components are 1013 + 2*k for k = 0, ..., 21, cf. A120214) and one cycle of length 45 with 4-digit components (least component is 1057, cf. A120215). Furthermore there are 22 cycles of length 1890 (least components are 100013 + 2*k for k = 0, ..., 21, cf. A120216), one cycle of length 945 (least component is 100057, cf. A120217) and 225 cycles of length 900 (least components are 100103 + 2*k for k = 0, ..., 224, cf. A120218), all having 6-digit components. It is conjectured that there are also cycles of increasing length with 8-, 10-, 12-, ... digit components. - Klaus Brockhaus, Jun 10 2006
From Michael S. Branicky, May 11 2023: (Start)
There are 22 cycles of length 19890 (least components are 10000013 + 2*k for k = 0, ..., 21), one cycle of length 9945 (least component 10000057), 225 cycles of length 18900 (least components are 10000103 + 2*k for k = 0, ..., 224) and 2250 cycles of length 9000 (least components are 10001003 + 2*k for k = 0, ..., 2249), all having 8-digit components.
These patterns continue.  Specifically, there is one cycle of length 10^(n/2) - 55 (least component 10^(n-1) + 57), and there are 22 cycles of length 2*(10^(n/2) - 55) (least components 10^(n-1) + 13 + 2*k for k = 0, ..., 21), each for n = 4, 6, 8, 10, 12, 14, 16. (End)

Michael S. Branicky, Python program for OEIS A118514, A118515, and A118516
N. J. A. Sloane and others, Sequences of RADD type, OEIS wiki.

For records see A118515, A118516. Cf. A117831. S_1 is A117521.

S_1013 is A120214, S_1057 is A120215, S_100013 is A120216, S_100057 is A120217, S_100103 is A120218.

Python
```
# see linked program
```

A117830 Let S_m be the infinite sequence formed by starting with m and repeatedly reversing the digits and adding 4 to get the next term. For all m < 1015, S_m enters the cycle of length 54 whose terms are shown here.

Original entry on oeis.org

5, 9, 13, 35, 57, 79, 101, 105, 505, 509, 909, 913, 323, 327, 727, 731, 141, 145, 545, 549, 949, 953, 363, 367, 767, 771, 181, 185, 585, 589, 989, 993, 403, 308, 807, 712, 221, 126, 625, 530, 39, 97, 83, 42, 28, 86, 72, 31, 17, 75, 61, 20, 6, 10, 5, 9, 13, 35, 57, 79, 101, 105, 505, 509, 909, 913, 323, 327, 727, 731, 141, 145

Offset: 1

Luc Stevens (lms022(AT)yahoo.com), Apr 06 2006

S_1015 is the first exception: this immediately enters the cycle of length 90 shown in A117807. - Klaus Brockhaus, May 05 2006

Except for the initial 1, identical to A117828.

N. J. A. Sloane and others, Sequences of RADD type, OEIS wiki.
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

S_1 is given in A117828, S_3 in A117829. See also A117827, A117831, A117807.

a(n) = A117828(n+1). - M. F. Hasler, May 22 2014

Edited by N. J. A. Sloane, May 05 2006

A118517 Define sequence S_m by: initial term = m, reverse digits and add 3 to get next term. Entry shows S_1. This reaches a cycle of length 3 in 1 step.

Original entry on oeis.org

1, 4, 7, 10, 4, 7, 10, 4, 7, 10, 4, 7, 10, 4, 7, 10, 4, 7, 10, 4, 7, 10, 4, 7, 10, 4, 7, 10, 4, 7, 10, 4, 7, 10, 4, 7, 10, 4, 7, 10, 4, 7, 10, 4, 7, 10, 4, 7, 10, 4, 7, 10, 4, 7, 10, 4, 7, 10, 4, 7, 10, 4, 7, 10, 4, 7, 10, 4, 7, 10, 4, 7, 10, 4, 7, 10, 4, 7, 10, 4, 7, 10, 4, 7, 10, 4, 7, 10

Offset: 1

N. J. A. Sloane, May 06 2006

N. J. A. Sloane and others, Sequences of RADD type, OEIS wiki.
Index entries for linear recurrences with constant coefficients, signature (0, 0, 1).

Cf. A117831, A118518 on.

Join[{1},LinearRecurrence[{0,0,1},{4,7,10},90]] (* Ray Chandler, Jul 18 2015 *)

A118510 Define sequence S_m by: initial term = m, reverse digits and add 1 to get next term. It is conjectured that S_m always reaches a cycle of length 9, as in A117230. Sequence gives records for number of steps to reach cycle.

Original entry on oeis.org

1, 18, 19, 36, 37, 54, 55, 72, 73

Offset: 1

N. J. A. Sloane, May 06 2006

The values of m which take this many steps are 1, 11, 101, 1001, 10001, 100001, 1000001, 10000001, 100000001, ...

N. J. A. Sloane and others, Sequences of RADD type, OEIS wiki.

Records in A118511.

Cf. A117230, A117831, A118473, A118474.

a(n) = 1 + 9*(n-1) for odd n; a(n) = 9*n for even n. Recursion: a(1) = 1; a(2) = 18; a(n+1) = a(n-1) + 18. - (Klaus Brockhaus, Jul 28 2006)

a(5) to a(9) from Klaus Brockhaus, Jul 28 2006

A118512 Define sequence S_m by: initial term = m, reverse digits and add 1 to get next term. Entry shows S_11. This reaches a cycle of length 9 in 18 steps.

Original entry on oeis.org

11, 12, 22, 23, 33, 34, 44, 45, 55, 56, 66, 67, 77, 78, 88, 89, 99, 100, 2, 3, 4, 5, 6, 7, 8, 9, 10, 2, 3, 4, 5, 6, 7, 8, 9, 10, 2, 3, 4, 5, 6, 7, 8, 9, 10, 2, 3, 4, 5, 6, 7, 8, 9, 10, 2, 3, 4, 5, 6, 7, 8, 9, 10, 2, 3, 4, 5, 6, 7, 8, 9, 10, 2, 3, 4, 5, 6, 7, 8, 9, 10, 2, 3, 4, 5, 6, 7, 8, 9, 10

Offset: 1

N. J. A. Sloane, May 06 2006

N. J. A. Sloane and others, Sequences of RADD type, OEIS wiki.
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 1).

Cf. A118510, A117831, A117230.

NestList[FromDigits[Reverse[IntegerDigits[#]]]+1&,11,90] (* Harvey P. Dale, Oct 16 2011 *)
Join[{11,12,22,23,33,34,44,45,55,56,66,67,77,78,88,89,99,100},LinearRecurrence[{0,0,0,0,0,0,0,0,1},{2,3,4,5,6,7,8,9,10},72]] (* Ray Chandler, Jul 18 2015 *)
NestList[IntegerReverse[#]+1&,11,90] (* Harvey P. Dale, Oct 13 2024 *)

A118513 Define sequence S_m by: initial term = m, reverse digits and add 1 to get next term. Entry shows S_13. This reaches a cycle of length 9 in 15 steps.

Original entry on oeis.org

13, 32, 24, 43, 35, 54, 46, 65, 57, 76, 68, 87, 79, 98, 90, 10, 2, 3, 4, 5, 6, 7, 8, 9, 10, 2, 3, 4, 5, 6, 7, 8, 9, 10, 2, 3, 4, 5, 6, 7, 8, 9, 10, 2, 3, 4, 5, 6, 7, 8, 9, 10, 2, 3, 4, 5, 6, 7, 8, 9, 10, 2, 3, 4, 5, 6, 7, 8, 9, 10, 2, 3, 4, 5, 6, 7, 8, 9, 10, 2, 3, 4, 5, 6, 7, 8, 9, 10

Offset: 1

N. J. A. Sloane, May 06 2006

N. J. A. Sloane and others, Sequences of RADD type, OEIS wiki.
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 1).

Cf. A118510, A117831, A117230, A118512.

Join[{13,32,24,43,35,54,46,65,57,76,68,87,79,98,90},LinearRecurrence[{0,0,0,0,0,0,0,0,1},{10,2,3,4,5,6,7,8,9},73]] (* Ray Chandler, Jul 18 2015 *)
NestList[IntegerReverse[#]+1&,13,90] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 06 2019 *)

A118522 Define sequence S_n by: initial term = n, reverse digits and add 3 to get next term. It is conjectured that S_n always reaches a cycle. Sequence gives number of steps for S_n to reach a cycle.

Original entry on oeis.org

1, 3, 3, 0, 2, 2, 0, 1, 1, 0, 0, 0, 6, 0, 0, 0, 4, 0, 0, 3, 0, 0, 14, 0, 0, 0, 4, 0, 0, 3, 0, 0, 11, 5, 13, 10, 3, 6, 6, 1, 5, 5, 4, 0, 0, 4, 0, 0, 0, 2, 0, 0, 7, 0, 0, 12, 0, 0, 0, 2, 0, 0, 7, 0, 0, 9, 3, 11, 8, 1, 4, 4, 2, 3, 3, 2, 0, 0, 2, 0, 0, 0, 6, 0, 0, 5, 0, 0, 10, 0, 0, 0, 6, 0, 0

Offset: 1

N. J. A. Sloane, May 06 2006

Initial cycles have length 3 or 6.
From Lars Blomberg, Jan 15 2018: (Start)
For n < 10^8, the only cycles found are the following:
  [4,7,10]
  [18,84,51]
  [29,95,62]
  [11,14,44,47,77,80]
  [12,24,45,57,78,90]
  [15,54,48,87,81,21]
  [16,64,49,97,82,31]
  [19,94,52,28,85,61]
  [22,25,55,58,88,91]
  [26,65,59,98,92,32]
The union of all of them has 51 terms (= 3*3 + 7*6): [4, 7, 10, 11, 12, 14, 15, 16, 18, 19, 21, 22, 24, 25, 26, 28, 29, 31, 32, 44, 45, 47, 48, 49, 51, 52, 54, 55, 57, 58, 59, 61, 62, 64, 65, 77, 78, 80, 81, 82, 84, 85, 87, 88, 90, 91, 92, 94, 95, 97, 98] (End)

Lars Blomberg, Table of n, a(n) for n = 1..10000
N. J. A. Sloane and others, Sequences of RADD type, OEIS wiki.

For records see A118523, A118524. Cf. A117831. For S_1, S_2 etc. see A118517-A118521.

cp's OEIS Frontend

A118473 Records in A117831.

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A118474 Where records occur in A117831.

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A117521 Start with 1 and repeatedly reverse the digits and add 2 to get the next term.

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A118514 Define sequence S_n by: initial term = n, reverse digits and add 2 to get next term. It is conjectured that S_n always reaches a cycle. Sequence gives number of steps for S_n to reach a cycle.

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A117830 Let S_m be the infinite sequence formed by starting with m and repeatedly reversing the digits and adding 4 to get the next term. For all m < 1015, S_m enters the cycle of length 54 whose terms are shown here.

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A118517 Define sequence S_m by: initial term = m, reverse digits and add 3 to get next term. Entry shows S_1. This reaches a cycle of length 3 in 1 step.

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A118510 Define sequence S_m by: initial term = m, reverse digits and add 1 to get next term. It is conjectured that S_m always reaches a cycle of length 9, as in A117230. Sequence gives records for number of steps to reach cycle.

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A118512 Define sequence S_m by: initial term = m, reverse digits and add 1 to get next term. Entry shows S_11. This reaches a cycle of length 9 in 18 steps.

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A118513 Define sequence S_m by: initial term = m, reverse digits and add 1 to get next term. Entry shows S_13. This reaches a cycle of length 9 in 15 steps.

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Mathematica

A118522 Define sequence S_n by: initial term = n, reverse digits and add 3 to get next term. It is conjectured that S_n always reaches a cycle. Sequence gives number of steps for S_n to reach a cycle.

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