%I #22 Dec 06 2024 16:24:53

%S 10,12,13,14,15,16,17,18,20,21,23,24,25,26,27,29,30,31,32,34,35,36,38,

%T 40,41,42,43,45,47,50,51,52,53,54,56,60,61,62,63,65,70,71,72,74,80,81,

%U 83,90,92,100,102,103,104,105,106,107,108,110,112,113,114,115,116,117

%N Numbers which need one 'Reverse and Add' step to reach a palindrome.

%C The number of steps starts at 0, so palindromes (A002113) are excluded.

%C Numbers k such that A033665(k) = 1. - _Andrew Howroyd_, Dec 05 2024

%H Harry J. Smith, <a href="/A065206/b065206.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Res#RAA">Index entries for sequences related to Reverse and Add!</a>

%t Select[Range[10,120],!PalindromeQ[#]&&PalindromeQ[#+IntegerReverse[#]]&] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jun 14 2017 *)

%o (ARIBAS): function revadd_steps(k,stop: integer); var c,n,m,steps,rev: integer; begin n := 0; c := 0; while c < stop do m := n; rev := int_reverse(m); steps := 0; while steps < k and m <> rev do m := m + rev; rev := int_reverse(m); inc(steps); end; if steps = k and m = rev then write(n," "); inc(c); end; inc(n); end; end; revadd_steps(1,66).

%o (Haskell)

%o a065206 n = a065206_list !! (n-1)

%o a065206_list = filter ((== 1) . a136522 . a056964) a029742_list

%o -- _Reinhard Zumkeller_, Oct 14 2011

%o (PARI) isok(n,s=1)={for(k=0, s, my(r=fromdigits(Vecrev(digits(n)))); if(r==n, return(k==s)); n += r); 0} \\ _Andrew Howroyd_, Dec 05 2024

%Y Cf. A002113, A015976, A033665, A136522, A056964, A029742.

%Y Sequences for 2..12 steps needed are: A065207, A065208, A065209, A065210, A065211, A065212, A065213, A065214, A065215, A065216, A065217.

%K nonn,base

%O 1,1

%A _Klaus Brockhaus_, Oct 21 2001

%E Offset corrected by _Harry J. Smith_, Oct 13 2009