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 A016016 Number of iterations of Reverse and Add which lead to a palindrome, or -1 if no palindrome is ever reached. 11
 1, 1, 1, 1, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 1, 1, 1, 2, 1, 2, 2, 3, 1, 1, 1, 1, 2, 1, 2, 2, 3, 4, 1, 1, 1, 2, 1, 2, 2, 3, 4, 6, 1, 1, 2, 1, 2, 2, 3, 4, 6, 24, 1, 2, 1, 2, 2, 3, 4, 6, 24 (list; graph; refs; listen; history; text; internal format)
 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 J. Walker, Three Years Of Computing: Final Report On The Palindrome Quest Eric Weisstein's World of Mathematics, 196-Algorithm. Index entries for sequences related to Reverse and Add! 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 Cf. A033665, A023109, A006960, A061563, A240510. Sequence in context: A037806 A038082 A107740 * A345112 A063059 A214564 Adjacent sequences: A016013 A016014 A016015 * A016017 A016018 A016019 KEYWORD nonn,base,nice AUTHOR Robert G. Wilson v STATUS approved

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Last modified July 12 17:26 EDT 2024. Contains 374251 sequences. (Running on oeis4.)