A066144 In base 2: n sets a new record for the number of 'Reverse and Add' steps needed to reach a palindrome starting with n.

0, 2, 11, 19, 20, 74, 398, 779, 1062, 2329, 4189, 4280, 11278, 19962, 98318, 135137, 1051360, 1592930, 69226926, 4295054186, 4446008678, 17187271449, 18123849698

Offset: 1

Author

Klaus Brockhaus, Dec 08 2001

Keywords

• nonn
• base
• more

Comments

The analog of A065198 in base 2. Integers like 22, for which a palindrome is never reached (cf. A066059), are of course disregarded. A066145 gives the corresponding records.

Examples

			Starting with 74, 11 'Reverse and Add' steps are needed to reach a palindrome; starting with n < 74, less (at most 5) steps are needed.
		

Links

• Index entries for sequences related to Reverse and Add!

Crossrefs

Record setting values in base b: A077406 (b=3), A075686 (b=4), A306599 (b=8), A065198 (b=10), A348571 (Zeckendorf).

Cf. A062130, A066057, A066058, A066059, A066145.

Programs

Mathematica

limit = 10^4; (* Assumes that there is no palindrome if none is found before "limit" iterations *)
best = -1; Select[Range[0, 100000], (np = #; i = 0;
   While[np != IntegerReverse[np, 2] && i < limit,
    np = np + IntegerReverse[np, 2]; i++];
If[i >= limit, False, If[i > best, best = i; True]]) &] (* Robert Price, Oct 14 2019 *)

Extensions

Offset corrected and a(19)-a(23) from A.H.M. Smeets, Apr 30 2022