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A283833 For t >= 0, if 2^t + t - 3 <= n <= 2^t + t - 1 then a(n) = 2^t - 1, while if 2^t + t - 1 < n < 2^(t+1) + t - 3 then a(n) = 2^(t+1) + t - 2 - n. 1
1, 1, 1, 3, 3, 3, 2, 1, 7, 7, 7, 6, 5, 4, 3, 2, 1, 15, 15, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 31, 31, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 63, 63, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Michel Marcus, Table of n, a(n) for n = 0..4104

J.-P. Allouche, J. Shallit, On the subword complexity of the fixed point of a -> aab, b -> b, and generalizations, arXiv preprint arXiv:1605.02361 [math.CO], 2016. See Table 3.

EXAMPLE

1,1,1;

;

3,3,3;

2,1;

7,7,7;

6,5,4,3,2,1;

15,15,15;

14,13,12,11,10,9,8,7,6,5,4,3,2,1;

31,31,31;

30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,10,9,8,7,6,5,4,3,2,1;

63,63,63;

62,61,60,59,...

MAPLE

A283833 := proc(n)

    local t;

    if n =0 then

        return 1;

    end if;

    for t from 0 do

        if 2^t+t-3 <= n and n<= 2^t+t-1 then

            return 2^t-1 ;

        elif 2^t+t-1 <= n and n<= 2^(t+1)+t-3 then

            return 2^(t+1)+t-2-n ;

        end if;

    end do:

end proc: # R. J. Mathar, Mar 28 2017

MATHEMATICA

a[0] = 1; a[n_] := For[t = 0, True, t++, Which[2^t + t - 3 <= n && n <= 2^t + t - 1, Return[2^t - 1], 2^t + t - 1 <= n && n <= 2^(t + 1) + t - 3, Return[ 2^(t + 1) + t - 2 - n]]];

Table[a[n], {n, 0, 80}] (* Jean-Fran├žois Alcover, Dec 09 2017, from Maple *)

PROG

(PARI) a(n) = {if (n==0, return (1)); for (t=0, oo, if (((2^t+t-3) <= n) && (n <= 2^t+t-1), return (2^t-1)); if (((2^t+t-1) <= n) && (n <= 2^(t+1)+t-3), return (2^(t+1)+t-2-n)); ); } \\ Michel Marcus, Aug 21 2017

CROSSREFS

Cf. A145071.

Sequence in context: A239232 A153012 A275300 * A280759 A016651 A135877

Adjacent sequences:  A283830 A283831 A283832 * A283834 A283835 A283836

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Mar 24 2017

STATUS

approved

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Last modified November 18 02:07 EST 2019. Contains 329242 sequences. (Running on oeis4.)