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

1,2

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]

Formula

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

Prog

(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];

Crossrefs

Cf. A304107, A304109, A304111.

Sequence in context: A137512 A157943 A267098 * A051134 A347777 A037458

Adjacent sequences: A304107 A304108 A304109 * A304111 A304112 A304113

Keyword

nonn

Author

Antti Karttunen, May 13 2018

Status

approved