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A065207 Two 'Reverse and Add' steps are needed to reach a palindrome. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The number of steps starts at 0, so palindromes (cf. A002113) are excluded.
LINKS
Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harry J. Smith)
MATHEMATICA
trasQ[n_]:=Length[NestWhileList[IntegerReverse[#]+#&, n, !PalindromeQ[ #]&, 1, 5]] ==3; Select[Range[300], trasQ] (* Harvey P. Dale, Apr 13 2022 *)
PROG
(ARIBAS): revadd_steps(2, 58). For the definition of function revadd_steps see A065206.
(PARI)
Rev(x)= { local(d, r=0); while (x>0, d=x-10*(x\10); x\=10; r=r*10 + d); return(r) }
digitsIn(x)= { local(d); if (x==0, return(1)); d=1 + log(x)\log(10); if (10^d == x, d++, if (10^(d-1) > x, d--)); return(d) }
Palin(x)= { local(d, e, f, i, t, y); if (x==0, return(1)); y=x; d=digitsIn(x); t=10^(d - 1); for (i=1, d\2, f=y-10*(y\10); y\=10; e=x\t; x-=t*e; t/=10; if (e!=f, return(0)) ); return(1) }
{ n=0; for (m = 0, 10^9, p=m; b=1; for (i=1, 2, if (Palin(p), b=0; break); p=Rev(p) + p); if (b && Palin(p), write("b065207.txt", n++, " ", m); if (n==1000, return)) ) } \\ Harry J. Smith, Oct 14 2009
(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
CROSSREFS
Sequence in context: A173639 A091448 A067777 * A084364 A094677 A052224
KEYWORD
nonn,base
AUTHOR
Klaus Brockhaus, Oct 21 2001
EXTENSIONS
Offset changed from 0 to 1 by Harry J. Smith, Oct 14 2009
STATUS
approved

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Last modified July 12 08:52 EDT 2024. Contains 374239 sequences. (Running on oeis4.)