OFFSET
0,2
COMMENTS
The analog of A023109 in base 2.
LINKS
EXAMPLE
11 is the smallest integer which requires two steps to reach a base 2 palindrome (cf. A066057), so a(2) = 11; written in base 10: 11 -> 11 + 13 = 24 -> 24 + 3 = 27; written in base 2: 1011 -> 1011 + 1101 = 11000 -> 11000 + 11 = 11011.
MATHEMATICA
Table[ SelectFirst[Range[0, 20000], (np = #; i = 0;
While[ np != IntegerReverse[np, 2] && i <= n,
np = np + IntegerReverse[np, 2]; i++];
i == n ) &] , {n, 0, 44}] (* Robert Price, Oct 16 2019 *)
PROG
(ARIBAS): For function b2reverse see A066057; function a066058(mx: integer); var k, m, n, rev, steps: integer; begin for k := 0 to mx do n := 0; steps := 0; m := n; rev := b2reverse(m); while not(steps = k and m = rev) do inc(n); m := n; rev := b2reverse(m); steps := 0; while steps < k and m <> rev do m := m + rev; rev := b2reverse(m); inc(steps); end; end; write(n, ", "); end; end; a066058(45).
(Python)
def A066058(n):
....if n > 0:
........k = 0
........while True:
............m = k
............for i in range(n):
................s1 = format(m, 'b')
................s2 = s1[::-1]
................if s1 == s2:
....................break
................m += int(s2, 2)
............else:
................s1 = format(m, 'b')
................if s1 == s1[::-1]:
....................return k
............k += 1
....else:
........return 0 # Chai Wah Wu, Jan 06 2015
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Klaus Brockhaus, Dec 04 2001
STATUS
approved