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A268678 Distinct values in A268395; partial sums of A268679.

%I A268678 #12 Feb 13 2016 23:16:43
%S A268678 0,1,3,4,5,7,8,11,15,16,18,19,20,22,23,26,27,31,32,34,36,37,40,41,42,
%T A268678 47,48,50,52,53,56,57,59,60,64,65,66,69,70,72,74,75,81,82,83,86,87,89,
%U A268678 90,92,93,98,101,102,104,105,106,108,109,113,116,117,119,120,121,123,124,127,131,132,134,135,136,138,139,142
%N A268678 Distinct values in A268395; partial sums of A268679.
%H A268678 Antti Karttunen, <a href="/A268678/b268678.txt">Table of n, a(n) for n = 0..32768</a>
%F A268678 a(0) = 0, for n >= 1, a(n) = A268679(n) + a(n-1).
%F A268678 a(n) = A268395(A001969(1+n)).
%F A268678 Other identities. For all n >= 0:
%F A268678 A268680(a(n)) = n.
%t A268678 f[n_] := Which[n == 1, 0, OddQ@ #, 0, EvenQ@ #, 1 + f[#/2]] &@ Fold[BitXor, n, Quotient[n, 2^Range[BitLength@ n - 1]]]; Union@ Accumulate@ Array[f, {150}] (* _Michael De Vlieger_, Feb 12 2016, after _Jan Mangaldan_ at A006068 *)
%o A268678 (Scheme, two variants, the first one using also memoizing-macro definec)
%o A268678 (definec (A268678 n) (if (zero? n) n (+ (A268679 n) (A268678 (- n 1)))))
%o A268678 (define (A268678 n) (A268395 (A001969 (+ 1 n))))
%Y A268678 Cf. A001969, A268395, A268679.
%Y A268678 Cf. A268677 (complement).
%Y A268678 Cf. A268680 (least monotonic left inverse).
%Y A268678 Cf. A268712.
%Y A268678 Cf. also A004128.
%K A268678 nonn
%O A268678 0,3
%A A268678 _Antti Karttunen_, Feb 10 2016