a(n) = min(k > a(n1)  A206925(k) = A206925(a(n1))), if this minimum exists, else a(n) = min(k >= 2*2^floor(log(a(n1)))  A206925(k) = min(A206925(j)  j >= 2*2^floor(log(a(n1)))).
A206925(a(n)) = 2*floor(log_2(a(n))).
A070939(a(n)) = 4 + floor((n4)/6), for n>4.
A206925(a(n)) = 6 + 2*floor((n4)/6), for n>4.
Iteration formulas for k>0:
a(6(k+1)+4) = 2a(6k+4) + floor(37*2^(k+5)/63) mod 2.
a(6(k+1)+5) = 2a(6k+5) + floor(41*2^(k+1)/63) mod 2.
a(6(k+1)+6) = 2a(6k+6) + floor(41*2^(k+5)/63) mod 2.
a(6(k+1)+7) = 2a(6k+7) + floor(37*2^(k+2)/63) mod 2.
a(6(k+1)+8) = 2a(6k+8) + floor(37*2^(k+4)/63) mod 2.
a(6(k+1)+9) = 2a(6k+9) + floor(41*2^(k+4)/63) mod 2.
Calculation formulas for k>0:
a(6k+4) = floor((37*2^(k+4)/63) mod 2^(k+4).
a(6k+5) = floor((41*2^(k+6)/63) mod 2^(k+4).
a(6k+6) = floor((41*2^(k+4)/63) mod 2^(k+4).
a(6k+7) = floor((37*2^(k+7)/63) mod 2^(k+4).
a(6k+8) = floor((37*2^(k+9)/63) mod 2^(k+4).
a(6k+9) = floor((41*2^(k+9)/63) mod 2^(k+4).
With q(i) = 1  2*(floor((i+5)/6)  floor((i+4)/6) + floor((i+2)/6) + floor(i/6)),
this means q(i) = 1, 1, 1, 1, 1, 1, for i = 1..6,
p(i) =  4 + 9*floor((i+5)/6)  4*floor((i+4)/6) + 4*floor((i+3)/6)  3*floor((i+2)/6)) + 2*floor((i+1)/6)),
this means p(i) = 5, 1, 5, 2, 4, 4, for i = 1..6,
k := k(n) = floor((n4)/6),
j := j(n) = 1 + (n4) mod 6,
we get the following formulas:
a(n+6) = 2*a(n) + floor((39+2*q(j))*2^(k+p(j))/63) mod 2, for n>9.
a(n+6) = 2*a(n) + b(k(n),j(n)), for n>9,
where b(k,j) is the 6x6matrix:
(1 0 1 0 0 0)
(1 1 1 1 1 1)
(0 0 0 0 1 1)
(0 0 1 1 0 0)
(1 1 0 0 1 0)
(1 0 1 0 0 0).
a(n) = floor((39+2*q(j(n)))*2^(k(n)+p(j(n))+5)/63) mod 2^(k(n)+4), for n>4.
a(n) = (floor((39+2*q(j))*2^(6+p(j))/63) mod 32) * 2^(k1) + (floor((39+2*q(j))*2^(6+p(j))/63) mod 64) * 2^(k mod 6 1)*(2^(6*floor(k/6))  1)/63 + sum_{i=1..(k mod 6  1)} 2^(k mod 6  1  i)*(floor((39+2*q(j))*2^(p(j)+i)/63) mod 2), for n>9.
a(n) = floor((39+2*q(j(n)))*2^(p(j(n))+floor((n+26)/6))/63) mod 2^floor((n+20)/6)), for n>4.
With: b(i) = floor((39+2*q(i))*2^(6+p(i))/63) mod 32, this means b(i) = 18, 19, 20, 22, 25, 26, for i = 1..6,
c(i) = (floor((39+2*q(i))*2^(6+p(i))/63) mod 64. This means c(i) = 50, 19, 52, 22, 25, 26, for i = 1..6:
a(n) = b(j)* 2^(k1) + c(j)*2^(k mod 6 1)*(2^(6*floor(k/6))  1)/63 + sum_{i=1..(k mod 6  1)} 2^(k mod 6  1  i)*(floor(c(j)*2^i/63) mod 2), for n>9.
a(n) = floor(16*c(j)*2^floor((n+2)/6)/63) mod (8*2^floor((n+2)/6))), for n>4.
Asymptotic behavior:
a(n) = O(2^(n/6)).
lim inf a(n)/2^floor((n+2)/6) = 8*37/63 = 4.698412….
lim sup a(n)/2^floor((n+2)/6) = 8*52/63 = 6.603174….
lim inf a(n)/2^(n/6) = sqrt(2)*4*52/63 = 4.66914953….
lim sup a(n)/2^(n/6) = 2^(1/3)*8*37/63 = 5.91962906….
G.f. g(x) = x*(2 + 4x + 5x^2 + 6x^3 + 9x^4 + 10x^5 + 7x^6 + 3x^8 + 6x^9 + x^10 + x^13)/(12x^6) + (x^16*(1+x^2)(1+x^27) + x^22*(1x^6)/(1x) + x^32*(1x^12)/((1x^2)(1x)) + x^47*(1+x^3)/(1x))/(1x^36).
Also: g(x) = x*(2 + 5x*(1x^40) + 4x^2*(1+x^2+x^3x^6x^36x^38x^42)+ 2x^3*(1x^3+x^6x^7+x^39+x^43)  6x^7*(1+x^4+x^38x^40)  x^12*(1x+x^7x^8x^10+x^15+x^16+x^18x^20x^23x^24)  3x^37*(1x^6))/((1x)(1+x^2)(1x^9)(1+x^9)(1+x^18)).
