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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. 9
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

Palindromes themselves are also 'Reverse and Add!'ed!

It is conjectured that a(196) = -1 - see A006860, A023108.

Because A061563 has offset 0 one should add a(0) = 1 here. - Wolfdieter Lang, Jan 12 2018

LINKS

T. D. Noe, Table of n, a(n) for n = 1..195

Index entries for sequences related to Reverse and Add!

J. Walker, Three Years Of Computing: Final Report On The Palindrome Quest

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

CROSSREFS

Cf. A033665, A023109, A006960, A061563, A240510.

Sequence in context: A037806 A038082 A107740 * A063059 A214564 A102675

Adjacent sequences:  A016013 A016014 A016015 * A016017 A016018 A016019

KEYWORD

nonn,base,nice,changed

AUTHOR

Robert G. Wilson v

STATUS

approved

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Last modified May 24 06:53 EDT 2019. Contains 323529 sequences. (Running on oeis4.)