A117816 -id:A117816 - cp's OEIS frontend

A117817 Let T_n be the infinite sequence formed by starting with 1 and repeatedly reversing the digits and adding n to get the next term. If T_n eventually reaches a cycle, sequence gives length of that cycle, otherwise -1.

9, 81, 3, 54, 207, 30, 63, 27, 1, -1, 9, 15, 18, 72, -1, 90, 54, 13, 18, -1, 15, 9, 9, 36, 45, 18, 9, 36, 18, -1, 9, 9, 3, 36, 72, 2, 27, 18, 3, -1, 18, 57, 63, 9, 22, 90, 18, 30, 54, -1, 6, 99, 54, 13, 36, 207, 12, 63, 45, -1, 36, 27, 30, 108, 36, 264, 99, 36, 3, -1, 18, 22, 45, 90, 12, 45, 117, 192, 18, -1, 36, 45, 63, 168, 1008, 36, 24, 306, 9, -1, 99, 639, 36, 54, 144, 18, 225, 468, 1, -1, 18, 300, 189, 171, 765, 90, 45, 462, 90, -1, 9, 513, 63, 69

Offset: 1

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

a(multiple of 10) = -1 (see A117816). a(15) = -1 (see A118532). a(n) is a multiple of 9/gcd(9,n) unless it is -1. - Martin Fuller, May 12 2006

For a discussion of the -1 entries see A117816.

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

See A117817 for the -1 entries and cross-references to T_1 through T_16.

ReverseNum[n_] := FromDigits[Reverse[IntegerDigits[n]]]; maxLen=10000; Table[z=1; lst={1}; While[z=ReverseNum[z]+n; !MemberQ[lst,z] && Length[lst]

a(21)-a(33) from Luc Stevens, May 08 2006

a(33) onwards from T. D. Noe and Martin Fuller, May 10 2006

A117831 Let S_n be the infinite sequence formed by starting with n and repeatedly reversing the digits and adding 4 to get the next term. Sequence gives number of steps for S_n to reach a cycle, or -1 if no cycle is ever reached.

Original entry on oeis.org

1, 1, 40, 7, 0, 0, 39, 6, 0, 0, 38, 5, 0, 18, 37, 3, 0, 43, 10, 0, 4, 42, 9, 4, 4, 41, 7, 0, 47, 40, 0, 8, 46, 13, 0, 8, 45, 11, 0, 7, 44, 0, 12, 50, 17, 3, 12, 49, 15, 1, 11, 48, 1, 16, 36, 3, 0, 16, 35, 1, 0, 41, 8, 2, 2, 40, 7, 2, 2, 39, 5, 0, 45, 12, 0, 6, 44, 11, 0, 6, 43, 9, 0, 49, 42, 0, 10

Offset: 1

N. J. A. Sloane, following discussions with Luc Stevens, May 03 2006

It is conjectured that S_n always reaches a cycle.

There are 22 different cycles of length 90 with 4-digit components. I guess that at most half of the numbers between 1000 and 10000 lead to the cycle of length 54 shown in A117830. - Klaus Brockhaus, May 05 2006

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

S_1 is given in A117828, S_3 in A117829, S_1015 in A117807.
Records are in A118473, A118474.
Full list of sequences on this topic (1): A117230, A117521, A117800, A117816, A117817, A117827, A117828, A117829, A117830, A117831 (this sequence)
Full list of sequences on this topic (2): A117837, A117841, A118473, A118474, A118510, A118511, A118512, A118513, A118514, A118515, A118516
Full list of sequences on this topic (3): A118517-A118533, A118535

V:= Vector(10^5,-1):
f:= proc(n)
  local L, H, S, i, j,found,x,y;
  global V;
  S:= {n}: H:= n; x:= n;
  for i from 1 to 10^5 do
    if V[x] > -1 then
       for j from 1 to i-1 do V[H[j]]:= i-j+V[x] od;
       return V[n];
    fi;
    L:= convert(x,base,10);
    x:= add(L[-j]*10^(j-1),j=1..nops(L)) + 4;
    if member(x, S) then
      found:= false; y:= 0;
      V[x]:= 0;
      for j from i by -1 to 1 do
        if H[j] = x then found:= true
        elif not found then V[H[j]]:= 0
        else y:= y+1; V[H[j]]:= y;
        fi
      od;
      return V[n]
    fi;
    H:= H, x;
    S:= S union {x};
  od;
end proc:
map(f, [$1..200]); # Robert Israel, May 07 2020

Corrected and extended by Klaus Brockhaus, May 05 2006

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

A117230 Start with 1 and repeatedly reverse the digits and add 1 to get the next term.

Original entry on oeis.org

1, 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, 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, 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, 1).

Cf. A117830, A117521, A117828, A117800, A117816, A117817.

read transforms; t1:=[1]; for n from 1 to 80 do t1:=[op(t1),1+digrev(t1[n])]; od:

Join[{1},LinearRecurrence[{0,0,0,0,0,0,0,0,1},{2,3,4,5,6,7,8,9,10},99]] (* Ray Chandler, Jul 18 2015 *)

a(n)=if(n>1,(n-2)%9+2,1) \\ M. F. Hasler, May 22 2014

Has period 9.

G.f.: -x*(9*x^9 +9*x^8 +8*x^7 +7*x^6 +6*x^5 +5*x^4 +4*x^3 +3*x^2 +2*x +1) / ((x -1)*(x^2 +x +1)*(x^6 +x^3 +1)). - Colin Barker, May 23 2014

Correction to the terms of the sequence (inserted missing term) Jeremy Gardiner, Jun 17 2010

A118533 Start with 1 and repeatedly reverse the digits and add 16 to get the next term.

Original entry on oeis.org

1, 17, 87, 94, 65, 72, 43, 50, 21, 28, 98, 105, 517, 731, 153, 367, 779, 993, 415, 530, 51, 31, 29, 108, 817, 734, 453, 370, 89, 114, 427, 740, 63, 52, 41, 30, 19, 107, 717, 733, 353, 369, 979, 995, 615, 532, 251, 168, 877, 794, 513, 331, 149, 957

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, 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, 0, 1).

Cf. A117828, A117816, A117817.

NestList[FromDigits[Reverse[IntegerDigits[#]]]+16&,1,60] (* Harvey P. Dale, Jul 19 2011 *)

After 721 steps enters a cycle of length 90.

A117841 Start with 1 and repeatedly reverse the digits and add 10 to get the next term.

Original entry on oeis.org

1, 11, 21, 22, 32, 33, 43, 44, 54, 55, 65, 66, 76, 77, 87, 88, 98, 99, 109, 911, 129, 931, 149, 951, 169, 971, 189, 991, 209, 912, 229, 932, 249, 952, 269, 972, 289, 992, 309, 913, 329, 933, 349, 953, 369, 973, 389, 993, 409, 914, 429, 934, 449, 954, 469, 974, 489, 994, 509

Offset: 1

David Applegate, May 05 2006

This sequence (unlike A117828, say) never cycles.

The operation can never generate a trailing zero and so is reversible. So it loops only if it returns to the start, which is impossible. - Martin Fuller, May 12 2006

Harvey P. Dale and N. J. A. Sloane, Table of n, a(n) for n = 1..20000 (First 1000 terms from Harvey P. Dale)
N. J. A. Sloane and others, Sequences of RADD type, OEIS wiki.

Cf. A117830, A117828, A117816, A117817.

NestList[FromDigits[Reverse[IntegerDigits[#]]]+10&,1,60] (* Harvey P. Dale, May 19 2012 *)
NestList[IntegerReverse[#]+10&,1,60] (* Harvey P. Dale, May 29 2025 *)

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

Original entry on oeis.org

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

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.

A118535 Start with 1 and repeatedly reverse the digits and add 20 to get the next term.

Original entry on oeis.org

1, 21, 32, 43, 54, 65, 76, 87, 98, 109, 921, 149, 961, 189, 1001, 1021, 1221, 1241, 1441, 1461, 1661, 1681, 1881, 1901, 1111, 1131, 1331, 1351, 1551, 1571, 1771, 1791, 1991, 2011, 1122, 2231, 1342, 2451, 1562, 2671, 1782, 2891, 2002, 2022

Offset: 1

N. J. A. Sloane, May 07 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.

NestList[IntegerReverse[#]+20&,1,50] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 14 2020 *)

Never reaches a cycle (see A117816).

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

cp's OEIS Frontend

A117817 Let T_n be the infinite sequence formed by starting with 1 and repeatedly reversing the digits and adding n to get the next term. If T_n eventually reaches a cycle, sequence gives length of that cycle, otherwise -1.

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A117831 Let S_n be the infinite sequence formed by starting with n and repeatedly reversing the digits and adding 4 to get the next term. Sequence gives number of steps for S_n to reach a cycle, or -1 if no cycle is ever reached.

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Maple

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A117230 Start with 1 and repeatedly reverse the digits and add 1 to get the next term.

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A118533 Start with 1 and repeatedly reverse the digits and add 16 to get the next term.

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A117841 Start with 1 and repeatedly reverse the digits and add 10 to get the next term.

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

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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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A118535 Start with 1 and repeatedly reverse the digits and add 20 to get the next term.

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