

A025280


Complexity of n: number of 1's required to build n using +, * and ^.


18



1, 2, 3, 4, 5, 5, 6, 5, 5, 6, 7, 7, 8, 8, 8, 6, 7, 7, 8, 8, 9, 9, 10, 8, 7, 8, 6, 7, 8, 9, 10, 7, 8, 9, 10, 7, 8, 9, 10, 10, 11, 11, 12, 11, 10, 11, 12, 9, 8, 9, 10, 10, 11, 8, 9, 9, 10, 10, 11, 11, 12, 12, 11, 7, 8, 9, 10, 11, 12, 12, 13, 9, 10, 10, 10, 11, 12, 11, 12, 11, 7, 8, 9, 10, 11, 12, 11
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OFFSET

1,2


REFERENCES

R. K. Guy, Unsolved Problems Number Theory, Sect. F26.


LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000
R. K. Guy, Some suspiciously simple sequences, Amer. Math. Monthly 93 (1986), 186190; 94 (1987), 965; 96 (1989), 905.
J. Iraids, K. Balodis, J. Cernenoks, M. Opmanis, R. Opmanis and K. Podnieks, Integer Complexity: Experimental and Analytical Results. arXiv preprint arXiv:1203.6462, 2012.  From N. J. A. Sloane, Sep 22 2012
Index to sequences related to the complexity of n


FORMULA

a(n) = A005208(n) + 1.


MAPLE

with(numtheory):
a:= proc(n) option remember; `if`(n=1, 1, min(
seq(a(i)+a(ni), i=1..n1),
seq(a(d)+a(n/d), d=divisors(n) minus {1, n}),
seq(a(root(n, p))+a(p), p=divisors(igcd(seq(i[2],
i=ifactors(n)[2]))) minus {0, 1})))
end:
seq(a(n), n=1..100); # Alois P. Heinz, Mar 08 2013


MATHEMATICA

root[x_, n_] := With[{f = FactorInteger[x]}, Times @@ (f[[All, 1]]^(f[[All, 2]]/n))]; Clear[a]; a[n_] := a[n] = If[n == 1, 1, Min[Table[a[i] + a[ni], {i, 1, n1}], Table[a[d] + a[n/d], {d, Divisors[n][[2 ;; 2]]}], Table[a[root[n, p]] + a[p], {p, DeleteCases[Divisors[GCD @@ FactorInteger[n][[All, 2]]], 01]}]]]; Table[a[n], {n, 1, 100}] (* JeanFrançois Alcover, Mar 12 2014, after Alois P. Heinz *)


CROSSREFS

Cf. A003037, A005245, A005520, A005208.
Sequence in context: A323727 A091334 A306560 * A096365 A319412 A200311
Adjacent sequences: A025277 A025278 A025279 * A025281 A025282 A025283


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, David W. Wilson


STATUS

approved



