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A182021 Achromatic number of n-cycle. 1
3, 2, 3, 3, 3, 4, 4, 5, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 7, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 9, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 13, 12, 13 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

REFERENCES

Hare, W. R.; Hedetniemi, S. T.; Laskar, R.; Pfaff, J. Complete coloring parameters of graphs. Proceedings of the sixteenth Southeastern international conference on combinatorics, graph theory and computing (Boca Raton, Fla., 1985). Congr. Numer. 48 (1985), 171--178. MR0830709 (87h:05088)

LINKS

Table of n, a(n) for n=3..80.

FORMULA

Let s_m = m^2/2 if m even, m(m-1)/2 if m odd. For m >= 0, the s_m sequence is 0, 0, 2, 3, 8, 10, 18, 21, 32, 36, 50, ... (A093353 with a different offset).

Suppose s_m <= n < s_{m+1}. If m is odd and n = s_m + 1 then a(n) = m-1, otherwise a(n) = m.

MAPLE

A093353 := proc(n)

    if n < 1 then

        0;

    else

        (n + modp(n, 2))*(n+1)/2 ;

    end if;

end proc:

A182021 := proc(n)

    for m from 0 do

        sm := A093353(m-1) ;

        if sm >  n then

            m := m-1 ;

            sm := A093353(m-1) ;

            if type(m, 'odd') and n = sm+1 then

                return m-1 ;

            else

                return m;

            end if;

        end if;

    end do:

end proc:

seq(A182021(n), n=3..80) ; # R. J. Mathar, Jul 12 2013

CROSSREFS

Sequence in context: A265705 A205237 A086920 * A117451 A130970 A144733

Adjacent sequences:  A182018 A182019 A182020 * A182022 A182023 A182024

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Apr 06 2012

STATUS

approved

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Last modified October 17 21:17 EDT 2021. Contains 348065 sequences. (Running on oeis4.)