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A005421 Number of numbers of complexity n.
(Formerly M0430)
11
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 (list; graph; refs; listen; history; text; internal format)
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, 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-Fran├žois Alcover, Aug 30 2018 *)

CROSSREFS

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

Sequence in context: A144176 A307686 A077418 * A306156 A276125 A208611

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

STATUS

approved

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Last modified December 14 14:50 EST 2019. Contains 329979 sequences. (Running on oeis4.)