OFFSET
1,5
COMMENTS
A first 'Reverse and Add' operation is always made, even if the starting value n is already a palindrome, in contrast to the variant A033665.
It is conjectured that a(196) = -1, see A023108.
Because A061563 has offset 0 one should add a(0) = 1 here. - Wolfdieter Lang, Jan 12 2018
Record indices and values beyond a(1) = 1 and a(5) = 2 are given in A065198 and A065199: These refer to the variant A033665 (main entry with more up-to-date references), as can be seen from A065199(1..3) = (0, 1, 2) for A065198(1..3) = (0, 10, 19). But all larger records correspond to a non-palindromic index n, in which case a(n) = A033665(n). - M. F. Hasler, Feb 16 2020
LINKS
T. D. Noe, Table of n, a(n) for n = 1..195
Eric Weisstein's World of Mathematics, 196-Algorithm.
EXAMPLE
6 -> 6 + 6 = 12 -> 12 + 21 = 33 is palindromic, took 2 steps so a(6)=2.
n = 89 needs 24 steps to end up with the palindrome 8813200023188. See A240510. - Wolfdieter Lang, Jan 12 2018
MATHEMATICA
tol = 1000; r[n_] := FromDigits[Reverse[IntegerDigits[n]]]; palQ[n_] := n == r[n]; ar[n_] := n + r[n]; Table[k = 0; If[palQ[n], n = ar[n]; k = 1]; While[! palQ[n] && k < tol, n = ar[n]; k++]; If[k == tol, k = -1]; k, {n, 98}] (* Jayanta Basu, Jul 11 2013 *)
With[{nn = 10^3}, Array[-1 + Length@ NestWhileList[# + IntegerReverse@ # &, #, ! PalindromeQ@ # &, {2, 1}, 10^3] /. k_ /; k == nn -> -1 &, 200, 0]] (* Michael De Vlieger, Jan 11 2018 *)
PROG
(PARI) a(n) = my(x=n, i=0); while(1, x=x+eval(concat(Vecrev(Str(x)))); i++; if(x==eval(concat(Vecrev(Str(x)))), return(i))) \\ Felix Fröhlich, Jan 12 2018
(PARI) A016016(n, LIM=exponent(n+1)*5)={-!for(i=0, LIM, my(r=A004086(n)); n==r&&i&&return(i); n+=r)} \\ with {A004086(n)=fromdigits(Vecrev(digits(n)))}. The second optional arg is a search limit, with default value chosen according to known records A065199 and indices A065198. - M. F. Hasler, Feb 16 2020
CROSSREFS
KEYWORD
nonn,base,nice
AUTHOR
STATUS
approved
