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A025280
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Complexity of n: number of 1's required to build n using +, * and ^.
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16
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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
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1,2
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REFERENCES
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R. K. Guy, Unsolved Problems Number Theory, Sect. F26.
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 1..10000
R. K. Guy, Some suspiciously simple sequences, Amer. Math. Monthly 93 (1986), 186-190; 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
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FORMULA
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a(n) = A005208(n) + 1.
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MAPLE
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with(numtheory):
a:= proc(n) option remember; `if`(n=1, 1, min(
seq(a(i)+a(n-i), i=1..n-1),
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
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MATHEMATICA
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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[n-i], {i, 1, n-1}], 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]]], 0|1]}]]]; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Mar 12 2014, after Alois P. Heinz *)
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CROSSREFS
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Cf. A003037, A005245, A005520, A005208.
Sequence in context: A154940 A133344 A091334 * A096365 A319412 A200311
Adjacent sequences: A025277 A025278 A025279 * A025281 A025282 A025283
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, David W. Wilson
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STATUS
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approved
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