A293976 - OEIS

%I #13 Dec 23 2024 14:53:45

%S 0,1,2,3,5,6,9,10,15,16,22,23,32,33,43,44,59,60,76,77,99,100,123,124,

%T 156,157,190,191,234,235,279,280,339,340,400,401,477,478,555,556,655,

%U 656,756,757,880,881,1005,1006,1162,1163,1320,1321,1511,1512,1703

%N a(2n) = a(2n-1) + a(n) for n >= 1, a(2n+1) = a(2n) + 1, a(0) = 0.

%C A variant of A033485.

%C Starting with a(1) = 1, the sequence can also be defined as the smallest increasing sequence equal to the sequence of differences between pairs of terms: a(n) = a(2n) - a(2n-1).

%C See A293977 for a variant which is not monotonic but a permutation of the nonnegative integers.

%H E. Angelini, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2010-June/004987.html">Successive weighing scales</a>, post to the SeqFan list, June 14, 2010.

%H E. Angelini, <a href="http://www.cetteadressecomportecinquantesignes.com/Roberval.htm">Weighing scales and sequences</a>.

%o (PARI) A293976_vec(n,A=List(1))=for(i=1,n\2,listput(A,A[#A]+A[i]);listput(A,A[#A]+1));concat(0,Vec(A))

%Y Cf. A033485, A293977.

%K nonn

%O 0,3

%A _M. F. Hasler_, Oct 27 2017