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 A066133 In base 2, twelve 'Reverse and Add' steps are needed to reach a palindrome. 1

%I

%S 1027,1139,1181,1229,1433,1481,1537,1649,1951,1983,1999,2031,2051,

%T 3073,3103,3215,3351,3463,3611,3639,3671,3723,3751,3783,3839,3859,

%U 3971,4087,4103,4121,4141,4187,4237,4269,4327,4331,4333,4361,4427,4603,4625,4645

%N In base 2, twelve 'Reverse and Add' steps are needed to reach a palindrome.

%C The analog of A065217 in base 2. The number of steps starts at 0, so palindromes (cf. A006995) are excluded.

%H Harry J. Smith, <a href="/A066133/b066133.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>

%o (PARI) Rev(x)= { local(d, r=0); while (x>0, d=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) } baseE(x, b)= { local(d, e=0, f=1); while (x>0, d=x-b*(x\b); x\=b; e+=d*f; f*=10); return(e) } baseI(x, b)= { local(d, e=0, f=1); while (x>0, d=x-10*(x\10); x\=10; e+=d*f; f*=b); return(e) } calcB(p)= { local(b,r); b=baseE(p, 2); r=Rev(b); d=baseI(r, 2) + p; b=baseE(d, 2); return(b); } { n=0; for (m=1, 10^9, d=m; t=1; b=baseE(d, 2); for (i=1, 12, if (Palin(b), t=0; break); b=calcB(d)); if (t && Palin(b), write("b066133.txt", n++, " ", m); if (n==1000, return)) ) } \\ _Harry J. Smith_, Feb 01 2010

%Y Cf. A006995, A065217, A066122.

%K base,nonn

%O 1,1

%A _Klaus Brockhaus_, Dec 08 2001

%E OFFSET changed from 0,1 to 1,1 by _Harry J. Smith_, Feb 01 2010

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Last modified May 16 14:24 EDT 2021. Contains 343949 sequences. (Running on oeis4.)