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A043261 Sum of the binary digits of the n-th base 2 palindrome. 1
0, 1, 2, 2, 3, 2, 4, 2, 3, 4, 5, 2, 4, 4, 6, 2, 3, 4, 5, 4, 5, 6, 7, 2, 4, 4, 6, 4, 6, 6, 8, 2, 3, 4, 5, 4, 5, 6, 7, 4, 5, 6, 7, 6, 7, 8, 9, 2, 4, 4, 6, 4, 6, 6, 8, 4, 6, 6, 8, 6, 8, 8, 10, 2, 3, 4, 5, 4, 5, 6, 7, 4, 5, 6, 7, 6, 7, 8, 9, 4, 5, 6, 7, 6, 7, 8, 9, 6, 7, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

Let b(1) = 0, b(2) = 1, otherwise b(2n-1) = b(n-1) and b(2n) = b(n)

Let c(1) = 0, c(2) = 1, otherwise c(2n-1) = c(n-1)+1 and c(2 n) =  c(n)

Then for n >= 2, a(2n-1) = 2 c(2n-1) - b(2n-1) and a(2 n) = 2 c(2 n)

EXAMPLE

The fourth base 2 palindrome is 5 = 101_2, so a(4) = 1+0+1=2.

MAPLE

b:= proc(n) option remember;

  procname(floor(n/2)) end proc;

b(1):= 0; b(2):= 1;

c:= proc(n) option remember;

  procname(floor(n/2)) + (n mod 2) end proc;

c(1):= 0; c(2):= 1;

A043261:= n -> 2*c(n) - (n mod 2)*b(n);

A043261(2):= 1; # Robert Israel, Apr 06 2014

CROSSREFS

Cf. A006995 (base 2 palindromes), A057148.

Sequence in context: A073182 A282446 A049599 * A157986 A025479 A093640

Adjacent sequences:  A043258 A043259 A043260 * A043262 A043263 A043264

KEYWORD

nonn,base

AUTHOR

Clark Kimberling

EXTENSIONS

edited by Robert Israel, Apr 06 2014

STATUS

approved

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Last modified April 28 00:46 EDT 2017. Contains 285556 sequences.