A078677 Write n in binary; repeatedly sum the "digits" until reaching 1; a(n) = sum of these sums (including '1' and n itself).

1, 3, 6, 5, 8, 9, 13, 9, 12, 13, 17, 15, 19, 20, 20, 17, 20, 21, 25, 23, 27, 28, 28, 27, 31, 32, 32, 34, 34, 35, 39, 33, 36, 37, 41, 39, 43, 44, 44, 43, 47, 48, 48, 50, 50, 51, 55, 51, 55, 56, 56, 58, 58, 59, 63, 62, 62, 63, 67, 65, 69, 70, 72, 65, 68, 69, 73, 71, 75, 76, 76, 75

Offset

1,2

Links

Table of n, a(n) for n=1..72.

Formula

a(n) = 1 (if n = 1); a(n) = n + a("occurrence of digit 1 in n(binary)") else;

Example

a(13)=19 because 13 = (1101) -> (1+1+0+1 = 11) -> (1+1 = 10) -> (1+0 = 1) = 1 and 1101+11+10+1(binary) = 19(decimal).

Crossrefs

Cf. A078627.

Sequence in context: A241474 A259556 A063520 * A059770 A019690 A010620

Adjacent sequences: A078674 A078675 A078676 * A078678 A078679 A078680

Keyword

base,easy,nonn

Author

Frank Schwellinger (nummer_eins(AT)web.de), Dec 17 2002

Status

approved