A118514 -id:A118514 - cp's OEIS frontend

A118515 Records in A118514.

1, 3, 9, 10, 15, 16, 17, 64, 5317, 5324, 5325, 5326, 5327, 5332, 5333, 10268, 512105, 512112, 512113, 512114, 512115, 512120, 512121, 1007106, 51026173, 51026180, 51026181, 51026182, 51026183, 51026188, 51026189, 100526174

Offset: 1

N. J. A. Sloane, May 06 2006

Rémy Sigrist, C program
N. J. A. Sloane and others, Sequences of RADD type, OEIS wiki.

Cf. A118514, A118516.

C
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See Links section.
```
Python
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# See linked program in A118514.
```

a(10) to a(25) from Klaus Brockhaus, Jun 12 2006

a(26) to a(32) from Rémy Sigrist, Aug 13 2022

A118516 Where records occur in A118514.

Original entry on oeis.org

1, 2, 12, 15, 25, 32, 102, 105, 111, 295, 392, 1002, 1918, 2187, 5812, 10009, 10011, 29995, 39992, 100002, 199918, 219987, 589912, 1000009, 1000011, 2999995, 3999992, 10000002, 19999918, 21999987, 58999912, 100000009

Offset: 1

N. J. A. Sloane, May 06 2006

All terms so far enter the cycle of length 81, cf. A117521. - Klaus Brockhaus, Jun 12 2006

Rémy Sigrist, C program
N. J. A. Sloane and others, Sequences of RADD type, OEIS wiki.

Cf. A118514, A118515.

C
```
See Links section.
```
Python
```
# See linked program in A118514.
```

a(10) to a(25) from Klaus Brockhaus, Jun 12 2006

a(26) to a(32) from Rémy Sigrist, Aug 13 2022

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

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.

A120214 Start with 1013 and repeatedly reverse the digits and add 2 to get the next term.

Original entry on oeis.org

1013, 3103, 3015, 5105, 5017, 7107, 7019, 9109, 9021, 1211, 1123, 3213, 3125, 5215, 5127, 7217, 7129, 9219, 9131, 1321, 1233, 3323, 3235, 5325, 5237, 7327, 7239, 9329, 9241, 1431, 1343, 3433, 3345, 5435, 5347, 7437, 7349, 9439, 9351, 1541, 1453, 3543

Offset: 1

Klaus Brockhaus, Jun 11 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(1013,2). 1013 is the first S for which T(S,2) reaches a cycle of length 90. The cycle is simply the first 90 terms, which then repeat. A full period is given in the table.

Klaus Brockhaus, Table of n, a(n) for n = 1,...,90
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. A117521, A118514, A120215, A120216, A120217, A120218.

NestList[IntegerReverse[#]+2&,1013,50] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 16 2016 *)

A120216 Start with 100013 and repeatedly reverse the digits and add 2 to get the next term.

Original entry on oeis.org

100013, 310003, 300015, 510005, 500017, 710007, 700019, 910009, 900021, 120011, 110023, 320013, 310025, 520015, 510027, 720017, 710029, 920019, 910031, 130021, 120033, 330023, 320035, 530025, 520037, 730027, 720039, 930029, 920041, 140031

Offset: 1

Klaus Brockhaus, Jun 11 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(100013,2). 100013 is the first S for which T(S,2) reaches a cycle of length 1890. The cycle is simply the first 1890 terms, which then repeat. A full period is given in the table.

Klaus Brockhaus, Table of n, a(n) for n = 1..1890
N. J. A. Sloane and others, Sequences of RADD type, OEIS wiki.
Index entries for linear recurrences with constant coefficients, order 1890.

Cf. A117521, A118514, A120214, A120215, A120217, A120218.

NestList[FromDigits[Reverse[IntegerDigits[#]]]+2&,100013,30] (* Harvey P. Dale, Oct 03 2014 *)

A120217 Start with 100057 and repeatedly reverse the digits and add 2 to get the next term.

Original entry on oeis.org

100057, 750003, 300059, 950005, 500061, 160007, 700063, 360009, 900065, 560011, 110067, 760013, 310069, 960015, 510071, 170017, 710073, 370019, 910075, 570021, 120077, 770023, 320079, 970025, 520081, 180027, 720083, 380029, 920085, 580031

Offset: 1

Klaus Brockhaus, Jun 11 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(100057,2). 100057 is the first S for which T(S,2) reaches a cycle of length 945. The cycle is simply the first 945 terms, which then repeat. A full period is given in the table.

Klaus Brockhaus, Table of n, a(n) for n = 1,...,945
N. J. A. Sloane and others, Sequences of RADD type, OEIS wiki.
Index entries for linear recurrences with constant coefficients, order 945.

Cf. A117521, A118514, A120214, A120215, A120216, A120218.

A120218 Start with 100103 and repeatedly reverse the digits and add 2 to get the next term.

Original entry on oeis.org

100103, 301003, 300105, 501005, 500107, 701007, 700109, 901009, 900111, 111011, 110113, 311013, 310115, 511015, 510117, 711017, 710119, 911019, 910121, 121021, 120123, 321023, 320125, 521025, 520127, 721027, 720129, 921029, 920131, 131031

Offset: 1

Klaus Brockhaus, Jun 11 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(100103,2). 100103 is the first S for which T(S,2) reaches a cycle of length 900. The cycle is simply the first 900 terms, which then repeat. A full period is given in the table.

Klaus Brockhaus, Table of n, a(n) for n = 1..900
N. J. A. Sloane and others, Sequences of RADD type, OEIS wiki.
Index entries for linear recurrences with constant coefficients, order 900.

Cf. A117521, A118514, A120214, A120215, A120216, A120217.

NestList[FromDigits[Reverse[IntegerDigits[#]]]+2&,100103,30] (* Harvey P. Dale, Aug 14 2012 *)

A120215 Start with 1057 and repeatedly reverse the digits and add 2 to get the next term.

Original entry on oeis.org

1057, 7503, 3059, 9505, 5061, 1607, 7063, 3609, 9065, 5611, 1167, 7613, 3169, 9615, 5171, 1717, 7173, 3719, 9175, 5721, 1277, 7723, 3279, 9725, 5281, 1827, 7283, 3829, 9285, 5831, 1387, 7833, 3389, 9835, 5391, 1937, 7393, 3939, 9395, 5941, 1497, 7943, 3499, 9945, 5501

Offset: 1

Klaus Brockhaus, Jun 11 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(1057,2). 1057 is the first S for which T(S,2) reaches a cycle of length 45. The cycle is simply the first 45 terms, which then repeat. A full period is shown.

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, 1).

Cf. A117521, A118514, A120214, A120216, A120217, A120218.

NestList[IntegerReverse[#]+2&,1057,50] (* Harvey P. Dale, Jan 25 2021 *)

a(n) = a(n-45). - Boštjan Gec, Sep 21 2023

cp's OEIS Frontend

A118515 Records in A118514.

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A118516 Where records occur in A118514.

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

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A120214 Start with 1013 and repeatedly reverse the digits and add 2 to get the next term.

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Mathematica

A120216 Start with 100013 and repeatedly reverse the digits and add 2 to get the next term.

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Mathematica

A120217 Start with 100057 and repeatedly reverse the digits and add 2 to get the next term.

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A120218 Start with 100103 and repeatedly reverse the digits and add 2 to get the next term.

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Mathematica

A120215 Start with 1057 and repeatedly reverse the digits and add 2 to get the next term.

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