cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 13 results. Next

A066122 Numbers that in base 2 need one 'Reverse and Add' step to reach a palindrome.

Original entry on oeis.org

2, 4, 6, 8, 10, 12, 14, 16, 18, 24, 30, 32, 34, 36, 38, 40, 42, 48, 52, 56, 62, 64, 66, 68, 70, 80, 82, 96, 100, 102, 112, 114, 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, 146, 148, 150, 160, 162, 168, 170, 176, 178, 192, 196, 198, 200, 204, 208, 212, 224
Offset: 1

Views

Author

Klaus Brockhaus, Dec 08 2001

Keywords

Comments

The analog of A065206 in base 2. The number of steps starts at 0, so palindromes (cf. A006995) are excluded.
Numbers k such that A066057(k) = 1. - Andrew Howroyd, Dec 05 2024

Links

Crossrefs

Cf. A006995, A065206, A066057.
Sequences for 2..12 steps needed are: A066123, A066124, A066125, A066126, A066127, A066128, A066129, A066130, A066131, A066132, A066133.

Programs

  • ARIBAS
    : function b2revadd_steps(k,stop: integer); var c,n,m,steps,rev: integer; begin n := 0; c := 0; while c < stop do m := n; rev := b2reverse(m); steps := 0; while steps < k and m <> rev do m := m + rev; rev := b2reverse(m); inc(steps); end; if steps = k and m = rev then write(n," "); inc(c); end; inc(n); end; end; b2revadd_steps(1,66).
  • PARI
    isok(n,s=1)={for(k=0, s, my(r=fromdigits(Vecrev(binary(n)),2)); if(r==n, return(k==s)); n += r); 0} \\ Andrew Howroyd, Dec 05 2024

Extensions

Offset changed from 0 to 1 by Harry J. Smith, Feb 01 2010

A015976 One iteration of Reverse and Add is needed to reach a palindrome.

Original entry on oeis.org

1, 2, 3, 4, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 36, 38, 40, 41, 42, 43, 44, 45, 47, 50, 51, 52, 53, 54, 56, 60, 61, 62, 63, 65, 70, 71, 72, 74, 80, 81, 83, 90, 92, 100, 101, 102, 103, 104, 105, 106
Offset: 1

Views

Author

Robert G. Wilson v

Keywords

Comments

The number of iterations starts at 1, so palindromes (cf. A002113) are not excluded. The corresponding sequence excluding palindromes is A065206.

Links

Crossrefs

Cf. A002113, A065206.

Programs

  • Haskell
    a015976 n = a015976_list !! (n-1)
a015976_list = filter ((== 1) . a136522 . a056964) [1..]
-- Reinhard Zumkeller, Oct 14 2011
  • Mathematica
    rev[n_] := FromDigits[Reverse[IntegerDigits[n]]]; Select[Range[106], rev[x = # + rev[#]] == x &] (* Jayanta Basu, Jul 24 2013 *)
Select[Range[120],PalindromeQ[#+IntegerReverse[#]]&] (* Harvey P. Dale, Jul 04 2022 *)

Extensions

Offset corrected by Reinhard Zumkeller, Oct 14 2011

A065207 Numbers which need two 'Reverse and Add' steps to reach a palindrome.

Original entry on oeis.org

19, 28, 37, 39, 46, 48, 49, 57, 58, 64, 67, 73, 75, 76, 82, 84, 85, 91, 93, 94, 109, 119, 129, 139, 149, 150, 152, 153, 154, 159, 160, 162, 163, 169, 170, 172, 173, 179, 189, 208, 218, 219, 228, 229, 238, 239, 248, 250, 251, 253, 258, 259, 260, 261, 268, 269
Offset: 1

Views

Author

Klaus Brockhaus, Oct 21 2001

Keywords

Comments

The number of steps starts at 0, so palindromes (cf. A002113) are excluded.
Numbers k such that A033665(k) = 2. - Andrew Howroyd, Dec 06 2024

Links

Crossrefs

Cf. A002113, A015977, A033665, A065206.

Programs

  • ARIBAS
    revadd_steps(2,58); (* For the definition of function revadd_steps see A065206. *)
  • Mathematica
    trasQ[n_]:=Length[NestWhileList[IntegerReverse[#]+#&,n,!PalindromeQ[ #]&,1,5]] ==3; Select[Range[300],trasQ] (* Harvey P. Dale, Apr 13 2022 *)
  • PARI
    isok(n,s=2)={for(k=0, s, my(r=fromdigits(Vecrev(digits(n)))); if(r==n, return(k==s)); n += r); 0} \\ Andrew Howroyd, Dec 06 2024
  • Python
    def ra(n): s = str(n); return int(s) + int(s[::-1])
def ispal(n): s = str(n); return s == s[::-1]
def aupto(limit):
  alst = []
  for k in range(limit+1):
    if ispal(k): continue
    k2 = ra(k)
    if ispal(k2): continue
    if ispal(ra(k2)): alst.append(k)
  return alst
print(aupto(269)) # Michael S. Branicky, May 06 2021

Extensions

Offset changed from 0 to 1 by Harry J. Smith, Oct 14 2009

A065208 Numbers which need three 'Reverse and Add' steps to reach a palindrome.

Original entry on oeis.org

59, 68, 86, 95, 155, 156, 157, 158, 164, 165, 168, 178, 180, 184, 185, 186, 194, 199, 249, 254, 255, 256, 257, 263, 264, 267, 277, 283, 284, 285, 293, 298, 299, 348, 349, 354, 355, 356, 362, 366, 376, 382, 384, 389, 392, 397, 398, 399, 439, 447, 448, 449, 452, 453, 455, 461, 462, 465, 475, 481, 482
Offset: 1

Views

Author

Klaus Brockhaus, Oct 21 2001

Keywords

Comments

The number of steps starts at 0, so palindromes (cf. A002113) are excluded.
Numbers k such that A033665(k) = 3. - Andrew Howroyd, Dec 06 2024

Links

Crossrefs

Cf. A002113, A015979, A033665, A065206.

Programs

  • ARIBAS
    revadd_steps(3,54). For the definition of function revadd_steps see A065206.
  • Mathematica
    palQ[n_]:=Module[{idn=IntegerDigits[n]},idn==Reverse[idn]]
tst[n_]:=palQ/@NestList[#+FromDigits[Reverse[IntegerDigits[#]]]&,n,3]=={False,False,False,True}
Select[Range[750],tst] (* Harvey P. Dale, Nov 26 2010 *)
  • PARI
    isok(n,s=3)={for(k=0, s, my(r=fromdigits(Vecrev(digits(n)))); if(r==n, return(k==s)); n += r); 0} \\ Andrew Howroyd, Dec 06 2024

Extensions

Offset changed from 0 to by Harry J. Smith, Oct 14 2009
More terms from Harvey P. Dale, Nov 26 2010

A065209 Numbers which need four 'Reverse and Add' steps to reach a palindrome.

Original entry on oeis.org

69, 78, 87, 96, 174, 175, 183, 192, 195, 273, 274, 280, 290, 291, 294, 372, 381, 390, 471, 472, 480, 492, 539, 570, 571, 579, 591, 599, 629, 638, 649, 670, 678, 679, 690, 698, 699, 728, 729, 748, 749, 769, 778, 789, 798, 819, 827, 836, 839, 847, 876, 877
Offset: 1

Views

Author

Klaus Brockhaus, Oct 21 2001

Keywords

Comments

The number of steps starts at 0, so palindromes (cf. A002113) are excluded.
Numbers k such that A033665(k) = 4. - Andrew Howroyd, Dec 06 2024

Links

Crossrefs

Cf. A002113, A015980, A033665, A065206.

Programs

Extensions

Offset changed from 0 to 1 by Harry J. Smith, Oct 14 2009

A065210 Numbers which need five 'Reverse and Add' steps to reach a palindrome.

Original entry on oeis.org

166, 176, 198, 265, 275, 297, 364, 374, 396, 463, 473, 495, 549, 562, 572, 594, 639, 648, 661, 671, 693, 738, 760, 770, 792, 837, 846, 891, 936, 945, 990, 1396, 1486, 1576, 1666, 1697, 1756, 1787, 1791, 1793, 1796, 1846, 1877, 1883, 1886, 1890, 1936
Offset: 1

Views

Author

Klaus Brockhaus, Oct 21 2001

Keywords

Comments

The number of steps starts at 0, so palindromes (cf. A002113) are excluded.
Numbers k such that A033665(k) = 5. - Andrew Howroyd, Dec 06 2024

Links

Crossrefs

Cf. A002113, A015982, A033665, A065206.

Programs

  • Mathematica
    palQ[k_]:=IntegerDigits[k]==Reverse[IntegerDigits[k]]; fraQ[n_]:= Module[ {ras=NestList[#+FromDigits[Reverse[IntegerDigits[#]]]&,n,5]},palQ/@ ras=={False,False,False,False,False,True}]; Select[Range[2000],fraQ] (* Harvey P. Dale, Sep 28 2015 *)

Extensions

Offset changed to 1 by Harry J. Smith, Oct 14 2009

A065211 Numbers which need six 'Reverse and Add' steps to reach a palindrome.

Original entry on oeis.org

79, 97, 182, 281, 380, 779, 799, 889, 977, 988, 997, 1069, 1079, 1159, 1169, 1249, 1259, 1339, 1349, 1429, 1439, 1519, 1529, 1609, 1619, 1699, 1709, 1789, 1799, 1879, 1889, 1896, 1969, 1979, 1986, 2059, 2068, 2078, 2089, 2149, 2158, 2168, 2179, 2239
Offset: 1

Views

Author

Klaus Brockhaus, Oct 21 2001

Keywords

Comments

The number of steps starts at 0, so palindromes (cf. A002113) are excluded.
Numbers k such that A033665(k) = 6. - Andrew Howroyd, Dec 06 2024

Links

Crossrefs

Cf. A002113, A015984, A033665, A065206.

Programs

  • Mathematica
    palQ[n_] := Module[{idn = IntegerDigits[n]}, idn == Reverse[idn]]; pal6Q[ n_]:= Module[{c=NestList[#+FromDigits[Reverse[IntegerDigits[#]]]&, n,6]}, palQ/@c=={False,False,False,False,False,False,True}]; Select[Range[ 2300],pal6Q] (* Harvey P. Dale, Sep 09 2012 *)

Extensions

Offset changed from 0 to 1 by Harry J. Smith, Oct 14 2009

A065212 Numbers which need seven 'Reverse and Add' steps to reach a palindrome.

Original entry on oeis.org

188, 190, 197, 287, 296, 386, 395, 485, 584, 593, 683, 692, 782, 791, 881, 890, 980, 1394, 1484, 1574, 1664, 1754, 1844, 1898, 1934, 1988, 1992, 1994, 1999, 2393, 2483, 2573, 2663, 2753, 2843, 2897, 2933, 2987, 2991, 2993, 2998, 3089, 3179, 3269, 3359
Offset: 1

Views

Author

Klaus Brockhaus, Oct 21 2001

Keywords

Comments

The number of steps starts at 0, so palindromes (cf. A002113) are excluded.
Numbers k such that A033665(k) = 7. - Andrew Howroyd, Dec 08 2024

Links

Crossrefs

Cf. A002113, A015986, A033665, A065206.

Programs

  • Mathematica
    lenQ[n_]:= Length[NestWhileList[# + FromDigits[Reverse[IntegerDigits[#]]]&, n,#!= FromDigits[Reverse[IntegerDigits[#]]]&, 1, 10]] == 8; Select[Range[500], lenQ] (* Vincenzo Librandi, Sep 24 2013 *)

Extensions

Offset changed from 0 to 1 by Harry J. Smith, Oct 14 2009

A065213 Numbers which need eight 'Reverse and Add' steps to reach a palindrome.

Original entry on oeis.org

193, 391, 490, 589, 688, 886, 985, 1993, 1995, 2994, 3991, 4990, 4992, 5991, 6990, 8059, 8149, 8239, 8329, 8419, 8509, 8599, 8689, 8779, 8869, 8959, 9058, 9069, 9089, 9148, 9159, 9179, 9238, 9249, 9269, 9328, 9359, 9418, 9429, 9508, 9519, 9539, 9598
Offset: 1

Views

Author

Klaus Brockhaus, Oct 21 2001

Keywords

Comments

The number of steps starts at 0, so palindromes (cf. A002113) are excluded.
Numbers k such that A033665(k) = 8. - Andrew Howroyd, Dec 08 2024

Links

Crossrefs

Cf. A002113, A015988, A033665, A065206.

Programs

  • Mathematica
    lenQ[n_]:=Length[NestWhileList[#+FromDigits[Reverse[IntegerDigits[#]]]&, n, #!=FromDigits[Reverse[IntegerDigits[#]]]&,1,10]]==9; Select[Range[ 10000], lenQ] (* Harvey P. Dale, Aug 09 2013 *)

Extensions

Offset changed from 0 to 1 by Harry J. Smith, Oct 14 2009

A065214 Numbers which need nine 'Reverse and Add' steps to reach a palindrome.

Original entry on oeis.org

1397, 1487, 1577, 1667, 1757, 1847, 1937, 2396, 2486, 2576, 2666, 2756, 2846, 2936, 2999, 3395, 3485, 3575, 3665, 3755, 3845, 3935, 3998, 4394, 4484, 4574, 4754, 4844, 4934, 4997, 5393, 5483, 5573, 5663, 5753, 5843, 5933, 5996, 6392, 6482, 6572
Offset: 1

Views

Author

Klaus Brockhaus, Oct 21 2001

Keywords

Comments

The number of steps starts at 0, so palindromes (cf. A002113) are excluded.
Numbers k such that A033665(k) = 9. - Andrew Howroyd, Dec 08 2024

Links

Crossrefs

Cf. A002113, A033665, A065206. Different from A015990.

Programs

  • Mathematica
    lenQ[n_]:= Length[NestWhileList[# + FromDigits[Reverse[IntegerDigits[#]]]&, n, #!= FromDigits[Reverse[IntegerDigits[#]]]&, 1, 10]] == 10; Select[Range[1000], lenQ] (* Vincenzo Librandi, Sep 24 2013 *)
Showing 1-10 of 13 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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