A033865 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

COMMENTS

It is believed that a(196) = -1.

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.

EXAMPLE

19 -> 19 + 91 = 110 -> 110 + 011 = 121, so a(19) = 121.

MATHEMATICA

Table[NestWhile[# + FromDigits[Reverse[IntegerDigits[#]]] &, n, IntegerDigits[#] != Reverse[IntegerDigits[#]] &], {n, 0, 90}] (* Harvey P. Dale, Dec 18 2011 *)

PROG

(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).

(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

CROSSREFS

Cf. A061563, A016016, A023109, A006960, A023108, A002113, A033665 (number of steps).

Sequence in context: A082273 A256755 A045876 * A364274 A118764 A226134

Adjacent sequences: A033862 A033863 A033864 * A033866 A033867 A033868

KEYWORD

nonn,base,nice

AUTHOR

David W. Wilson

EXTENSIONS

More terms from Jenise Smalley (neicey01(AT)hotmail.com), Oct 18 2001

STATUS

approved