A118878 -id:A118878 - cp's OEIS frontend

A119903 Records in A118878.

1, 190, 191, 192, 193, 8486, 16525, 16526, 16527, 16528, 16529, 16530, 825992, 1624591, 1624787, 1624983, 1625179, 1625375, 1625571, 1625767, 1625963, 1626159, 1626355, 1626391, 1626392, 1626393, 1626394, 1626395, 1626396, 82253978, 162059977, 162079973

Offset: 1

Klaus Brockhaus, May 28 2006

Rémy Sigrist, Table of n, a(n) for n = 1..56
Rémy Sigrist, C program
N. J. A. Sloane and others, Sequences of RADD type, OEIS wiki.

Cf. A117800, A118878, A119904.

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More terms from Rémy Sigrist, Aug 13 2022

A119904 Where records occur in A118878.

Original entry on oeis.org

1, 2, 15, 64, 95, 111, 119, 411, 604, 995, 1035, 4945, 10011, 10109, 10119, 10129, 10139, 10149, 10159, 10169, 10179, 10189, 10199, 11009, 40011, 60004, 99995, 100035, 499945, 1000011, 1001009, 1001019, 1001029, 1001039, 1001049, 1001059, 1001069, 1001079

Offset: 1

Klaus Brockhaus, May 28 2006

Rémy Sigrist, Table of n, a(n) for n = 1..56
Rémy Sigrist, C program
N. J. A. Sloane and others, Sequences of RADD type, OEIS wiki.

Cf. A117800, A118878, A119903.

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See Links section.
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More terms from Rémy Sigrist, Aug 13 2022

A117800 Start with 1 and repeatedly reverse the digits and add 5 to get the next term.

Original entry on oeis.org

1, 6, 11, 16, 66, 71, 22, 27, 77, 82, 33, 38, 88, 93, 44, 49, 99, 104, 406, 609, 911, 124, 426, 629, 931, 144, 446, 649, 951, 164, 466, 669, 971, 184, 486, 689, 991, 204, 407, 709, 912, 224, 427, 729, 932, 244, 447, 749, 952, 264, 467, 769, 972, 284, 487, 789, 992, 304, 408

Offset: 0

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

N. J. A. Sloane, Table of n, a(n) for n = 0..414 (shows two full cycles)
N. J. A. Sloane and others, Sequences of RADD type, OEIS wiki.
Index entries for linear recurrences with constant coefficients, order 207.

Cf. A117828, A118878, A118879.

NestList[IntegerReverse[#] + 5 &, 1, 100] (* Paolo Xausa, Aug 27 2024 *)

After 1 step enters a cycle of length 207.

It appears that there is a unique cycle of length 207 for the reverse-and-add-5 problem. Klaus Brockhaus has done an extensive search without finding any further cycle of length 207. There are many cycles of lengths 36 and 756. See A118878.

A118879 Let T(S,Q) be the sequence obtaining by starting with S and repeatedly reversing the digits and adding Q to get the next term. This is T(1016,5), the first S for which T(S,5) reaches a cycle of length 36.

Original entry on oeis.org

1016, 6106, 6021, 1211, 1126, 6216, 6131, 1321, 1236, 6326, 6241, 1431, 1346, 6436, 6351, 1541, 1456, 6546, 6461, 1651, 1566, 6656, 6571, 1761, 1676, 6766, 6681, 1871, 1786, 6876, 6791, 1981, 1896, 6986, 6901, 1101, 1016, 6106, 6021

Offset: 0

N. J. A. Sloane, May 26 2006

The cycle is simply the first 36 terms, which then repeat.

For S < 1016, T(S,5) reaches a cycle of length 207 (cf. A117800).

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, 1).

Cf. A117828, A117800, A118878.

NestList[IntegerReverse[#]+5&,1016,40] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 05 2020 *)

A119902 Start with 100016 and repeatedly reverse the digits and add 5 to get the next term.

Original entry on oeis.org

100016, 610006, 600021, 120011, 110026, 620016, 610031, 130021, 120036, 630026, 620041, 140031, 130046, 640036, 630051, 150041, 140056, 650046, 640061, 160051, 150066, 660056, 650071, 170061, 160076, 670066, 660081, 180071, 170086, 680076

Offset: 1

Klaus Brockhaus, May 28 2006

Let T(S,Q) be the sequence obtained by starting with S and repeatedly reversing the digits and adding Q to get the next term. This is T(10016,5). 100016 is the first S for which T(S,5) reaches a cycle of length 756. The cycle is simply the first 756 terms, which then repeat. A full period is given in the table.

Klaus Brockhaus, Table of n, a(n) for n = 1,...,756
N. J. A. Sloane and others, Sequences of RADD type, OEIS wiki.

Cf. A117800, A118879, A118878.

NestList[FromDigits[Reverse[IntegerDigits[#]]]+5&,100016,40]  (* Harvey P. Dale, Feb 24 2011 *)

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A119903 Records in A118878.

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A119904 Where records occur in A118878.

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A117800 Start with 1 and repeatedly reverse the digits and add 5 to get the next term.

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Formula

A118879 Let T(S,Q) be the sequence obtaining by starting with S and repeatedly reversing the digits and adding Q to get the next term. This is T(1016,5), the first S for which T(S,5) reaches a cycle of length 36.

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Mathematica

A119902 Start with 100016 and repeatedly reverse the digits and add 5 to get the next term.

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Author

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Links

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Programs

Mathematica