A293976 a(2n) = a(2n-1) + a(n) for n >= 1, a(2n+1) = a(2n) + 1, a(0) = 0.

0, 1, 2, 3, 5, 6, 9, 10, 15, 16, 22, 23, 32, 33, 43, 44, 59, 60, 76, 77, 99, 100, 123, 124, 156, 157, 190, 191, 234, 235, 279, 280, 339, 340, 400, 401, 477, 478, 555, 556, 655, 656, 756, 757, 880, 881, 1005, 1006, 1162, 1163, 1320, 1321, 1511, 1512, 1703

Offset: 0

Author

M. F. Hasler, Oct 27 2017

Keywords

• nonn

Comments

A variant of A033485.

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).

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

Links

• E. Angelini, Successive weighing scales, post to the SeqFan list, June 14, 2010.
• E. Angelini, Weighing scales and sequences.

Crossrefs

Cf. A033485, A293977.

Programs

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))