A065207 -id:A065207 - cp's OEIS frontend

A065206 Numbers which need one 'Reverse and Add' step to reach a palindrome.

10, 12, 13, 14, 15, 16, 17, 18, 20, 21, 23, 24, 25, 26, 27, 29, 30, 31, 32, 34, 35, 36, 38, 40, 41, 42, 43, 45, 47, 50, 51, 52, 53, 54, 56, 60, 61, 62, 63, 65, 70, 71, 72, 74, 80, 81, 83, 90, 92, 100, 102, 103, 104, 105, 106, 107, 108, 110, 112, 113, 114, 115, 116, 117

Offset: 1

Klaus Brockhaus, Oct 21 2001

The number of steps starts at 0, so palindromes (A002113) are excluded.

Numbers k such that A033665(k) = 1. - Andrew Howroyd, Dec 05 2024

Harry J. Smith, Table of n, a(n) for n = 1..1000
Index entries for sequences related to Reverse and Add!

Cf. A002113, A015976, A033665, A136522, A056964, A029742.

Sequences for 2..12 steps needed are: A065207, A065208, A065209, A065210, A065211, A065212, A065213, A065214, A065215, A065216, A065217.

function revadd_steps(k,stop: integer); var c,n,m,steps,rev: integer; begin n := 0; c := 0; while c < stop do m := n; rev := int_reverse(m); steps := 0; while steps < k and m <> rev do m := m + rev; rev := int_reverse(m); inc(steps); end; if steps = k and m = rev then write(n," "); inc(c); end; inc(n); end; end; revadd_steps(1,66).

a065206 n = a065206_list !! (n-1)
a065206_list = filter ((== 1) . a136522 . a056964) a029742_list
-- Reinhard Zumkeller, Oct 14 2011

Select[Range[10,120],!PalindromeQ[#]&&PalindromeQ[#+IntegerReverse[#]]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 14 2017 *)

isok(n,s=1)={for(k=0, s, my(r=fromdigits(Vecrev(digits(n)))); if(r==n, return(k==s)); n += r); 0} \\ Andrew Howroyd, Dec 05 2024

Offset corrected by Harry J. Smith, Oct 13 2009

A015977 Two iterations of Reverse and Add are needed to reach a palindrome.

Original entry on oeis.org

5, 6, 7, 8, 9, 19, 28, 37, 39, 46, 48, 49, 55, 57, 58, 64, 66, 67, 73, 75, 76, 82, 84, 85, 91, 93, 94, 109, 119, 129, 139, 149, 150, 151, 152, 153, 154, 159, 160, 161, 162, 163, 169, 170, 171, 172, 173, 179, 189, 208, 218, 219, 228, 229, 238, 239, 248

Offset: 0

Robert G. Wilson v

The number of iterations starts at 1, so palindromes (cf. A002113) are not excluded. The corresponding sequence excluding palindromes is A065207.

Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for sequences related to Reverse and Add!

Cf. A002113, A065207.

Select[Range[250],Boole[PalindromeQ/@Rest[NestList[#+IntegerReverse[#]&,#,2]]] == {0,1}&] (* Harvey P. Dale, May 11 2022 *)

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):
    k2 = ra(k)
    if ispal(k2): continue
    if ispal(ra(k2)): alst.append(k)
  return alst
print(aupto(250)) # Michael S. Branicky, May 06 2021

A066123 Numbers that in base 2 need two 'Reverse and Add' steps to reach a palindrome.

Original entry on oeis.org

11, 13, 23, 29, 39, 43, 53, 55, 57, 59, 69, 79, 81, 87, 91, 109, 117, 121, 133, 143, 151, 161, 167, 171, 173, 175, 179, 181, 183, 205, 207, 213, 215, 229, 233, 235, 237, 239, 241, 243, 245, 247, 261, 265, 277, 287, 289, 303, 311, 321, 327, 337, 343, 347, 349

Offset: 1

Klaus Brockhaus, Dec 08 2001

The analog of A065207 in base 2. The number of steps starts at 0, so palindromes (cf. A006995) are excluded.

Numbers k such that A066057(k) = 2. - Andrew Howroyd, Dec 05 2024

Harry J. Smith, Table of n, a(n) for n = 1..1000
Index entries for sequences related to Reverse and Add!

Cf. A006995, A065207, A066057, A066122.

isok(n,s=2)={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

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

A236689 The sum of two neighboring digits is a palindrome; a(n) is the smallest possible nonnegative integer not occurring earlier.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 10, 7, 11, 8, 12, 9, 20, 13, 14, 15, 16, 17, 18, 30, 21, 22, 23, 24, 25, 26, 27, 29, 200, 31, 32, 33, 34, 35, 36, 38, 100, 40, 41, 42, 43, 44, 45, 47, 101, 50, 51, 52, 53, 54, 56, 102, 60, 61, 62, 63, 65, 103, 80, 70, 71, 72, 74, 104

Offset: 0

Eric Angelini and M. F. Hasler, Jan 29 2014

The sum of two digits is a palindrome iff it is less than 10 or equal to 11. Therefore, numbers with substrings 19, 28, 37, 39, 46, ... (this is not A065207) can never occur, and this is not a permutation of the nonnegative integers.

E. Angelini, Palindromes -- with digits, SeqFan List, Jan 27 2014.

Cf. A228730.

a=u=0;(isp(s)=s<10||s==11);for(n=1,100,print1(a",");u+=1<1,d[j-1],a%10)+d[j])&&next;k=(k\10^(#d-j)+1)*10^(#d-j)-1;next(2));a=k;break))

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A065206 Numbers which need one 'Reverse and Add' step to reach a palindrome.

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A015977 Two iterations of Reverse and Add are needed to reach a palindrome.

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A066123 Numbers that in base 2 need two 'Reverse and Add' steps to reach a palindrome.

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A236689 The sum of two neighboring digits is a palindrome; a(n) is the smallest possible nonnegative integer not occurring earlier.

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PARI