A304110 a(n) is the number of terms of A304107 <= n; Partial sums of A304109.

1, 2, 3, 3, 3, 4, 5, 5, 6, 6, 7, 7, 8, 9, 9, 9, 9, 10, 11, 11, 11, 12, 13, 13, 14, 15, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 21, 21, 21, 22, 22, 23, 23, 23, 24, 25, 25, 26, 27, 27, 27, 28, 28, 29, 29, 29, 30, 31, 31, 32, 33, 33, 33, 33, 34, 35, 35, 35, 36, 37, 37, 38, 39, 39, 39, 40, 40, 41, 41, 41, 42, 43, 43, 43, 44

Offset: 1

Author

Antti Karttunen, May 13 2018

Keywords

• nonn

Comments

Question: Does lim_{n -> inf} a(n)/n converge to 1/2 ? See also A304111.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Index entries for sequences related to polynomials in ring GF(2)[X]

Crossrefs

Cf. A304107, A304109, A304111.

Programs

PARI

up_to = 128;
A304109(n) = { my(fm=factor(Pol(binary(n))*Mod(1, 2))); for(k=1, #fm~, if(fm[k, 2] > 1, return(0))); (1); };
prepare_v304110(up_to) = { my(v=vector(up_to), c=0); for(n=1, up_to, c += A304109(n); v[n] = c); (v); };
v304110 = prepare_v304110(up_to);
A304110(n) = v304110[n];

Formula

a(1) = 1; for n > 1, a(n) = A304109(n) + a(n-1).