%I #17 Aug 21 2023 16:44:25

%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 One 'Reverse and Add' step is needed to reach a palindrome.

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

%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 (PARI) Rev(x)= { local(d, r=0); while (x>0, d=x-10*(x\10); x\=10; r=r*10 + d); return(r) } digitsIn(x)= { local(d); if (x==0, return(1)); d=1 + log(x)\log(10); if (10^d == x, d++, if (10^(d-1) > x, d--)); return(d) } Palin(x)= { local(d,e,f,i,t,y); if (x==0, return(1)); y=x; d=digitsIn(x); t=10^(d - 1); for (i=1, d\2, f=y-10*(y\10); y\=10; e=x\t; x-=t*e; t/=10; if (e!=f, return(0)) ); return(1) } { n=0; for (m = 0, 10^9, if (!Palin(m) && Palin(Rev(m) + m), write("b065206.txt", n++, " ", m); if (n==1000, return)) ) } \\ _Harry J. Smith_, Oct 13 2009

%o (Haskell)

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

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

%o -- _Reinhard Zumkeller_, Oct 14 2011

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

%K nonn,base

%O 1,1

%A _Klaus Brockhaus_, Oct 21 2001

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