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A078677 Write n in binary; repeatedly sum the "digits" until reaching 1; a(n) = sum of these sums (including '1' and n itself). 0

%I #3 Feb 27 2009 03:00:00

%S 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,

%T 32,32,34,34,35,39,33,36,37,41,39,43,44,44,43,47,48,48,50,50,51,55,51,

%U 55,56,56,58,58,59,63,62,62,63,67,65,69,70,72,65,68,69,73,71,75,76,76,75

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

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

%e 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).

%Y Cf. A078627.

%K base,easy,nonn

%O 1,2

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

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