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

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

Author

Klaus Brockhaus, Oct 21 2001

Keywords

• nonn
• base

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

• Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harry J. Smith)
• Index entries for sequences related to Reverse and Add!

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