A117828 -id:A117828 - cp's OEIS frontend

A118532 Start with 1 and repeatedly reverse the digits and add 15 to get the next term.

1, 16, 76, 82, 43, 49, 109, 916, 634, 451, 169, 976, 694, 511, 130, 46, 79, 112, 226, 637, 751, 172, 286, 697, 811, 133, 346, 658, 871, 193, 406, 619, 931, 154, 466, 679, 991, 214, 427, 739, 952, 274, 487, 799, 1012, 2116, 6127, 7231, 1342, 2446

Offset: 1

N. J. A. Sloane, May 06 2006

This sequence never cycles.

The plot (see the Noe link) shows 2774 terms of this sequence. It has a regular structure, which continues at higher decades. - T. D. Noe, May 10 2006

T. D. Noe, Table of n, a(n) for n = 1..2774
T. D. Noe, Plot of A118532
N. J. A. Sloane and others, Sequences of RADD type, OEIS wiki.

Cf. A117828, A117816, A117817.

a118532 n = a118532_list !! (n-1)
a118532_list = iterate ((+ 15) . a004086) 1
-- Reinhard Zumkeller, Jan 29 2014

A118532(Nmax,Q=15,S=1)=vector(Nmax,i,if(i>1,S=A004086(S)+Q,S)) \\ - M. F. Hasler, May 06 2012

This sequence never cycles. After a while, the pattern of length changes settles into an increasing pattern: 10^(4m)+3, 10^(4m+1)+3, 10^(4m+2)+12, 10^(4m+3)+12, 10^(4(m+1))+3, ... The key is that every two steps adds 15 at each end, unless there is a carry across the middle or a trailing 0. This allows many steps to be carried out in a single operation. - Martin Fuller, May 12 2006

a(n+1) = A004086(a(n)) + 15. - Reinhard Zumkeller, Jan 29 2014

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 *)

A118529 Start with 1 and repeatedly reverse the digits and add 12 to get the next term.

Original entry on oeis.org

1, 13, 43, 46, 76, 79, 109, 913, 331, 145, 553, 367, 775, 589, 997, 811, 130, 43, 46, 76, 79, 109, 913, 331, 145, 553, 367, 775, 589, 997, 811, 130, 43, 46, 76, 79, 109, 913, 331, 145, 553, 367, 775, 589, 997, 811, 130, 43, 46, 76, 79, 109, 913, 331

Offset: 1

N. J. A. Sloane, May 06 2006

Harvey P. Dale, Table of n, a(n) for n = 1..1000
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, 1).

Cf. A117828, A117816, A117817.

NestList[IntegerReverse[#]+12&,1,60] (* Harvey P. Dale, Dec 16 2024 *)

After 2 steps enters a cycle of length 15.

A119454 Start with 34 and repeatedly reverse the digits and add 16 to get the next term.

Original entry on oeis.org

34, 59, 111, 127, 737, 753, 373, 389, 999, 1015, 5117, 7131, 1333, 3347, 7449, 9463, 3665, 5679, 9781, 1895, 5997, 8011, 1124, 4227, 7240, 443, 360, 79, 113, 327, 739, 953, 375, 589, 1001, 1017, 7117, 7133, 3333, 3349, 9449, 9465, 5665, 5681, 1881, 1897, 7997, 8013, 3124, 4229, 9240, 445, 560, 81

Offset: 1

Klaus Brockhaus, May 20 2006

Has period 54. A full period is shown.
There are infinitely many numbers that eventually reach this cycle (e.g. 8100). What is the smallest? - N. J. A. Sloane, May 21 2006
The smallest number that eventually reaches this cycle is 26 (cf. A119481). - Klaus Brockhaus, May 23 2006

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

Cf. A118533, A119451, A117828.

A007398 Add 7, then reverse digits.

Original entry on oeis.org

0, 7, 41, 84, 19, 62, 96, 301, 803, 18, 52, 95, 201, 802, 908, 519, 625, 236, 342, 943, 59, 66, 37, 44, 15, 22, 92, 99, 601, 806, 318, 523, 35, 24, 13, 2, 9, 61, 86, 39, 64, 17, 42, 94, 101, 801, 808, 518, 525, 235, 242, 942, 949, 659, 666, 376, 383, 93, 1, 8, 51, 85, 29, 63

Offset: 0

N. J. A. Sloane

From n = 1 the sequence is periodic with a period of 63. The Data without the initial 0 gives that period. - David A. Corneth, Aug 01 2018

J. Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 15.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Nick Hobson, Python program for this sequence
N. J. A. Sloane and others, Sequences of RADD type, OEIS wiki.

Cf. A117828.

rev:=proc(n) local nn, nnn: nn:=convert(n,base,10): add(nn[nops(nn)+1-j]*10^(j-1),j=1..nops(nn)) end: a[0]:=0: for n from 1 to 70 do a[n]:=rev(7+a[n-1]) od: seq(a[n],n=0..70); # Emeric Deutsch, Jul 28 2006

NestList[FromDigits[Reverse[IntegerDigits[# + 7]]]&, 0, 60] (* Vincenzo Librandi, Aug 08 2017 *)

first(n) =  my(res = vector(n)); res[1]=0; for(i = 2, n, res[i] = fromdigits(Vecrev(digits(res[i - 1] + 7)))); res \\ David A. Corneth, Aug 01 2018

More terms from Emeric Deutsch, Jul 28 2006

A118090 Start with 1 and repeatedly reverse the digits and add 44 to get the next term.

Original entry on oeis.org

1, 45, 98, 133, 375, 617, 760, 111, 155, 595, 639, 980, 133, 375, 617, 760, 111, 155, 595, 639, 980, 133, 375, 617, 760, 111, 155, 595, 639, 980, 133, 375, 617, 760, 111, 155, 595, 639, 980, 133, 375, 617, 760, 111, 155, 595, 639, 980, 133, 375, 617, 760

Offset: 1

Luc Stevens (lms022(AT)yahoo.com), May 11 2006

After 3 steps enters a cycle of length 9.

Harvey P. Dale, Table of n, a(n) for n = 1..1000
N. J. A. Sloane and others, Sequences of RADD type, OEIS wiki.

Cf. A117828, A117816, A117817.

NestList[IntegerReverse[#]+44&,1,60] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Feb 03 2021 *)

A118150 Start with 1 and repeatedly reverse the digits and add 53 to get the next term.

Original entry on oeis.org

1, 54, 98, 142, 294, 545, 598, 948, 902, 262, 315, 566, 718, 870, 131, 184, 534, 488, 937, 792, 350, 106, 654, 509, 958, 912, 272, 325, 576, 728, 880, 141, 194, 544, 498, 947, 802, 261, 215, 565, 618, 869, 1021, 1254, 4574, 4807, 7137, 7370, 790, 150, 104

Offset: 1

Luc Stevens (lms022(AT)yahoo.com), May 14 2006

After 49 steps enters a cycle of 54.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
N. J. A. Sloane and others, Sequences of RADD type, OEIS wiki.

Cf. A117828, A117816, A117817.

NestList[IntegerReverse[#]+53&,1,60] (* Harvey P. Dale, Sep 21 2023 *)

Corrected by Harvey P. Dale, Apr 19 2014

A118155 Start with 1 and repeatedly reverse the digits and add 59 to get the next term.

Original entry on oeis.org

1, 60, 65, 115, 570, 134, 490, 153, 410, 73, 96, 128, 880, 147, 800, 67, 135, 590, 154, 510, 74, 106, 660, 125, 580, 144, 500, 64, 105, 560, 124, 480, 143, 400, 63, 95, 118, 870, 137, 790, 156, 710, 76, 126, 680, 145, 600, 65, 115, 570, 134, 490, 153, 410

Offset: 1

Luc Stevens (lms022(AT)yahoo.com), May 14 2006

After 2 steps enters a cycle of 45.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
N. J. A. Sloane and others, Sequences of RADD type, OEIS wiki.

Cf. A117828, A117816, A117817.

NestList[FromDigits[Reverse[IntegerDigits[#]]]+59&,1,80] (* Harvey P. Dale, Feb 25 2014 *)

Corrected by Harvey P. Dale, Feb 25 2014

A118161 Start with 1 and repeatedly reverse the digits and add 55 to get the next term.

Original entry on oeis.org

1, 56, 120, 76, 122, 276, 727, 782, 342, 298, 947, 804, 463, 419, 969, 1024, 4256, 6579, 9811, 1244, 4476, 6799, 10031, 13056, 65086, 68111, 11241, 14266, 66296, 69321, 12451, 15476, 67506, 60631, 13661, 16686, 68716, 61841, 14871, 17896, 69926

Offset: 1

Luc Stevens (lms022(AT)yahoo.com), May 14 2006

After 1371 steps enters a cycle of 36.

Georg Fischer, Table of n, a(n) for n = 1..2000
N. J. A. Sloane and others, Sequences of RADD type, OEIS wiki.

Cf. A117828, A117816, A117817.

a(23) ff. corrected by Georg Fischer, Jul 17 2020

A118162 Start with 1 and repeatedly reverse the digits and add 60 to get the next term.

Original entry on oeis.org

1, 61, 76, 127, 781, 247, 802, 268, 922, 289, 1042, 2461, 1702, 2131, 1372, 2791, 2032, 2362, 2692, 3022, 2263, 3682, 2923, 3352, 2593, 4012, 2164, 4672, 2824, 4342, 2494, 5002, 2065, 5662, 2725, 5332, 2395, 5992, 3055, 5563, 3715, 5233, 3385, 5893, 4045

Offset: 1

Luc Stevens (lms022(AT)yahoo.com), May 14 2006

Harvey P. Dale, Table of n, a(n) for n = 1..1000
N. J. A. Sloane and others, Sequences of RADD type, OEIS wiki.

Cf. A117828, A117816, A117817.

NestList[IntegerReverse[#]+60&,1,50] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 10 2017 *)

Never reaches a cycle (see A117816).

cp's OEIS Frontend

A118532 Start with 1 and repeatedly reverse the digits and add 15 to get the next term.

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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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A118529 Start with 1 and repeatedly reverse the digits and add 12 to get the next term.

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A119454 Start with 34 and repeatedly reverse the digits and add 16 to get the next term.

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A007398 Add 7, then reverse digits.

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A118090 Start with 1 and repeatedly reverse the digits and add 44 to get the next term.

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Mathematica

A118150 Start with 1 and repeatedly reverse the digits and add 53 to get the next term.

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Mathematica

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A118155 Start with 1 and repeatedly reverse the digits and add 59 to get the next term.

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Mathematica

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A118161 Start with 1 and repeatedly reverse the digits and add 55 to get the next term.