A033865 Start with n; if palindrome, stop; otherwise add to itself with digits reversed; a(n) gives palindrome at which it stops, or -1 if no palindrome is ever reached.
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 11, 33, 44, 55, 66, 77, 88, 99, 121, 22, 33, 22, 55, 66, 77, 88, 99, 121, 121, 33, 44, 55, 33, 77, 88, 99, 121, 121, 363, 44, 55, 66, 77, 44, 99, 121, 121, 363, 484, 55, 66, 77, 88, 99, 55, 121, 363, 484, 1111, 66, 77, 88, 99, 121, 121, 66, 484, 1111, 4884, 77, 88, 99, 121, 121, 363, 484, 77, 4884, 44044, 88
Offset: 0
Examples
19 -> 19 + 91 = 110 -> 110 + 011 = 121, so a(19) = 121.
References
- M. Donner, I Love Me, Vol. I: S. Wordrow's palindromic encyclopedia (Algonquin Books, 1996) p. 268
Links
- T. D. Noe, Table of n, a(n) for n = 0..195
- O. Forster, ARIBAS
- Mathforum, Making Numbers into Palindromic Numbers
- Eric Weisstein's World of Mathematics, 196-Algorithm.
Programs
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ARIBAS
var st: stack; end; for k := 0 to 60 do n := k; while n <> int_reverse(n) do n := n + int_reverse(n); end; stack_push(st,n); end; stack2array(st);
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Mathematica
Table[NestWhile[# + FromDigits[Reverse[IntegerDigits[#]]] &, n, IntegerDigits[#] != Reverse[IntegerDigits[#]] &], {n, 0, 90}] (* Harvey P. Dale, Dec 18 2011 *) -
PARI
a(n)=my(k); while((k=fromdigits(Vecrev(digits(n)))) != n, n += k); n \\ infinite loop if a(n) = -1; Charles R Greathouse IV, Dec 13 2015
Extensions
More terms from Jenise Smalley (neicey01(AT)hotmail.com), Oct 18 2001
Comments