OFFSET
1,1
COMMENTS
Comment from Altug Alkan, Dec 03 2015: (Start) Except for 3, all terms are divisible by 6 (cf. A048702, A265027).
Proof: Binary palindromes of even length (A048701) are odd for n > 0. So A048701(n) - A048701(n-1) is an even number for n > 1. Because the length is even and palindromic numbers are symmetric, for any digit “1” that is related with 2^n in its expansion which n is even, there are another digit “1” that is related with 2^m in its expansion which m is odd. 2^n+2^m is always divisible by 3 if n is even and m is odd. Therefore A048701(n) is divisible by 3, so A048701(n) - A048701(n-1) is divisible by 3 for n > 0. In conclusion, A048701(n) - A048701(n-1) is always divisible by 6 for n > 1. (End)
LINKS
N. J. A. Sloane, Table of n, a(n) for n = 1..32767
FORMULA
PROG
(PARI) a048701(n) = my(f); f = length(binary(n)) - 1; 2^(f+1)*n + sum(i=0, f, bittest(n, i) * 2^(f-i));
vector(100, n, (a048701(n) - a048701(n-1))) \\ Altug Alkan, Dec 03 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 30 2015
STATUS
approved