0,2

a(n) is the length signature of a string plus its length.

The positive members of this sequence are exactly the numbers that can be expressed as the sum of two or more consecutive positive integers (cf. A138591). - David Wasserman (wasserma(AT)spawar.navy.mil), Jan 24 2002

Starting at 3, these are the positions of the check bits in the single-error-correcting Hamming code.

Except for the offset 0, sequence corresponds to numbers with at least an odd divisor. (For largest odd divisor see A000265.) - Lekraj Beedassy (blekraj(AT)yahoo.com), Apr 12 2005

These are exactly the numbers n with the property that, given the n(n-1)/2 sums of pairs, the original numbers can be recovered uniquely. [Nick Reingold, see Winkler reference.]

Subsequence of A158581; A000120(a(n)) > 1. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 16 2009]

P. Winkler, Mathematical Mind-Benders, Peters, Wellesley, MA, 2007; see p. 27.

R. Zumkeller, Table of n, a(n) for n = 0..10000 [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 16 2009]

a(n) = n + [log_2(n + [log_2(n)])] gives this sequence with the exception of a(1) = 1. - David W. Wilson, Mar 29 2005

Find k such that 2^k - (k + 1) <= n < 2^(k+1) - (k + 2), then a(n) = n + k + 1.

Numbers n=2a(k)-1 k>0 are such that sum_{k=0...n}B_kM(n-k)binomial(n, k)=0 where B_k is the k-th Bernoulli number and M_k the k-th Motzkin number - Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 19 2005

Complement of A000079. Cf. A057717, A001227, A138591.

See A074894 for more about the question of when the sums of n numbers taken k at a time determine the numbers.

Sequence in context: A010906 A114309 A079581 this_sequence A138591 A136492 A062506

Adjacent sequences: A057713 A057714 A057715 this_sequence A057717 A057718 A057719

nonn

John Lindgren (john.lindgren(AT)Eng.Sun.COM), Oct 24 2000

Better description from Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 29 2001