A174354 a(0)=1, a(1)=a(2)=2, a(3)=8 and for n >= 4: if n == 0 (mod 4), a(n)=2, if n == 1 (mod 4), a(n)=8, if n == 2 (mod 4), a(n)=2, if n == 3 (mod 8), a(n)=32, if n = 16k + 15, a(n) = 128*4^k, and if n = 16k+7, a(n) = 128*4^(k-1).

1, 2, 2, 8, 2, 8, 2, 32, 2, 8, 2, 32, 2, 8, 2, 128, 2, 8, 2, 32, 2, 8, 2, 128, 2, 8, 2, 32, 2, 8, 2, 512, 2, 8, 2, 32, 2, 8, 2, 512, 2, 8, 2, 32, 2, 8, 2, 2048, 2, 8, 2, 32, 2, 8, 2, 2048, 2, 8, 2, 32, 2, 8, 2, 8192, 2, 8, 2, 32, 2, 8, 2, 8192, 2, 8, 2, 32, 2, 8, 2, 32768, 2, 8, 2, 32, 2, 8, 2

Offset

0,2

Comments

It seems that this sequence gives the numbers of "2" in the successive sets of 2, which appear in A174353.

Links

Antti Karttunen, Table of n, a(n) for n = 0..16384

Example

a(7) = 32 because 7 = 16*(0) + 7 and a(7) = 128*4^(-1).
a(8) = 2 because 8 == 0 (mod 4).

Maple

A174354 := proc(n)
    if n  <= 3 then
        return op(n+1, [1, 2, 2, 8]) ;
    end if;
    if n mod 4 =0 then
        2  ;
    elif n mod 4 =1 then
        8  ;
    elif n mod 4 = 2 then
        2
    elif n mod 8 = 3 then
        32
    elif n mod 16 = 15 then
        128*4^((n-15)/16)
    elif n mod 16 =7 then
        128*4^((n-7)/16-1)
    end if;
end proc:
seq(A174354(n), n=0..240) ; # R. J. Mathar, Feb 29 2016

Mathematica

Nest[Append[#1, Which[Mod[#2, 4] == 0, 2, Mod[#2, 4] == 1, 8, Mod[#2, 4] == 2, 2, Mod[#2, 8] == 3, 32, Mod[#2, 16] == 15, 128*4^Quotient[#2, 16], True, 128*4^(Quotient[#2, 16] - 1)]] & @@ {#, Length@ #} &, {1, 2, 2, 8}, 91] (* Michael De Vlieger, Nov 06 2018 *)

Prog

(PARI) A174354(n) = if(n<=1, 1+n, if(3==n, 8, if(0==((n%4)%2), 2, if(1==(n%4), 8, if(3==(n%8), 32, if(15==(n%16), 128*4^((n-15)/16), 128*4^((n-7)/16-1))))))); \\ (Adapted from Maple-program) - Antti Karttunen, Nov 06 2018

Crossrefs

Cf. A174353.

Sequence in context: A343059 A161915 A342818 * A011147 A273168 A098818

Adjacent sequences: A174351 A174352 A174353 * A174355 A174356 A174357

Keyword

easy,nonn

Author

Richard Choulet, Mar 17 2010

Status

approved