1,2

The complexity of an integer n is the least number of 1's needed to represent it using only additions, multiplications, exponentiation and parentheses. This does not allow juxtaposition of 1's to form larger integers, so, for example, 2 = 1+1 has complexity 2, but 11 does not (concatenating two 1's is not an allowed operation). The complexity of a number has been defined in several different ways by different authors. See the Index to the OEIS for other definitions. - Jonathan Vos Post (jvospost3(AT)gmail.com), Oct 20 2007

W. A. Beyer, M. L. Stein and S. M. Ulam, The Notion of Complexity. Report LA-4822, Los Alamos Scientific Laboratory of the University of California, Los Alamos, NM, December 1971.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

An example (usually nonunique) of the derivation of the first 10 values.

a(1) = 1, the number of 1's in "1."

a(2) = 2, the number of 1's in "1+1 = 2."

a(3) = 3, the number of 1's in "1+1+1 = 3."

a(4) = 4, the number of 1's in "1+1+1+1 = 4."

a(5) = 5, the number of 1's in "1+1+1+1+1 = 5."

a(6) = 7, since there are 6 1's in "((1+1)*(1+1+1))+1 = 7."

a(7) = 11, since there are 7 1's in "((1+1+1)^(1+1))+1+1 = eleven."

a(8) = 13, since there are 8 1's in "((1+1+1)*(1+1+1+1))+1 = thirteen."

a(9) = 21, since there are 9 1's in "((1+1+1)*(((1+1)*(1+1+1))+1) = twenty-one."

a(10) = 23, since there are 10 1's in "1+((1+1)*(((1+1+1)^(1+1))+1+1)) = twenty-three."

Cf. A025280, A005520, A005245.

Cf. A025280, A005520, A005245, A005421, A117618.

Sequence in context: A046022 A073019 A007885 this_sequence A046420 A108318 A006456

Adjacent sequences: A003034 A003035 A003036 this_sequence A003038 A003039 A003040

nonn,nice

N. J. A. Sloane (njas(AT)research.att.com).

More terms from David W. Wilson (davidwwilson(AT)comcast.net) May 15 1997