A005421 Number of numbers of complexity n, i.e., that can be built from n ones using + and *, and require at least that many ones. (Formerly M0430)

1, 1, 1, 1, 2, 3, 2, 6, 6, 7, 14, 16, 20, 34, 42, 56, 84, 108, 152, 214, 295, 398, 569, 763, 1094, 1475, 2058, 2878, 3929, 5493, 7669, 10501, 14707, 20476, 28226, 39287, 54817, 75619, 105584, 146910, 203294, 283764, 394437, 547485, 763821, 1061367, 1476067, 2057708, 2861449

Offset

1,5

References

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

Links

Janis Iraids, Table of n, a(n) for n = 1..75

J. Arias de Reyna and J. van de Lune, The question "How many 1's are needed?" revisited, arXiv preprint arXiv:1404.1850 [math.NT], 2014.

Tim Peters, Python program to compute this sequence

D. A. Rawsthorne, How many 1's are needed?, Fib. Quart. 27 (1989), 14-17.

Eric Weisstein's World of Mathematics, Integer Complexity

Index to sequences related to the complexity of n

Mathematica

terms = 30;
kmax = 60000;
cpx[1] = 1; cpx[k_] := cpx[k] = Min[Sequence @@ Table[cpx[i] + cpx[k-i], {i, 1, k/2}], Sequence @@ Table[cpx[d] + cpx[k/d], {d, Divisors[k][[2 ;; -2]]}]];
Clear[a]; a[_] = 0;
Do[n = cpx[k]; a[n] += 1, {k, 1, kmax}];
Array[a, terms] (* Jean-François Alcover, Aug 30 2018 *)

Crossrefs

Cf. A005245 (complexity of n), A005520 (records).

Sequence in context: A144176 A307686 A077418 * A348083 A306156 A276125

Adjacent sequences: A005418 A005419 A005420 * A005422 A005423 A005424

Keyword

nonn,nice

Author

Simon Plouffe

Extensions

More terms from Tim Peters (tim.one(AT)comcast.net), Nov 12 2004

a(43)-a(75) from Janis Iraids, Apr 20 2011

Name clarified by Glen Whitney, Oct 05 2021

Status

approved