A298606 Partial sums of A293630.

1, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 15, 17, 18, 20, 21, 22, 23, 25, 26, 27, 29, 30, 31, 32, 33, 35, 36, 37, 38, 40, 41, 42, 44, 45, 46, 47, 48, 50, 51, 52, 53, 55, 56, 57, 59, 60, 61, 62, 64, 65, 67, 68, 69, 70, 72, 73, 74, 76, 77, 78, 79, 80, 82, 83, 84, 85

Offset

1,2

Comments

a(n) is n plus the number of 2's in A293630 on the interval 1..n.

Links

Iain Fox, Table of n, a(n) for n = 1..10369

Formula

a(A291481(n)) = A298590(n).

Lim_{k->infinity} a(k)/k = 1.275261... (see A296564).

a(n) ~ d*n, where d = 1.275261... (see A296564).

Example

A293630 begins 1, 2, 1, 1, 1, 2, 1, 1, 2, ... so:
a(1) = 1.
a(2) = 1 + 2 = 3.
a(3) = 1 + 2 + 1 = 4.
a(4) = 1 + 2 + 1 + 1 = 5.
...

Mathematica

Accumulate@ Nest[Join @@ {#, Join @@ ConstantArray[Most@ #, Last@ #]} &, {1, 2}, 5] (* Michael De Vlieger, Jan 22 2018 *)

Prog

(PARI) lista(nn) = my(v=[1, 2], l, w, s=0); for(n=1, nn, l=length(v); w=vector(l-1, i, v[i]); v=concat(v, if(v[l]-1, concat(w, w), w))); for(i=1, length(v), s += v[i]; print1(s, ", "))

Crossrefs

Cf. A291481, A293630, A296564, A298590.

Sequence in context: A122488 A241403 A287727 * A039095 A001957 A184484

Adjacent sequences: A298603 A298604 A298605 * A298607 A298608 A298609

Keyword

nonn

Author

Iain Fox, Jan 22 2018

Status

approved