A298474 a(n) is the least k such that A090701(k) = n.

1, 2, 6, 8, 11, 14, 18, 20, 24, 26, 30, 32, 36, 38, 42, 44, 48, 50, 54, 56, 60, 62, 66, 68, 72, 74, 78, 80, 84, 86, 90, 92, 96, 98, 102, 104, 108, 110, 114, 116, 120, 122, 126, 128, 132, 134, 138, 140, 144, 146, 150, 152, 156, 158, 162, 164, 168, 170, 174

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (1, 1, -1).

Formula

a(n) = floor(log_2(A298476(n))) + 1.

From Robert Israel, Jan 24 2018: (Start)

If n is even, a(n) = 3*n-4.

If n <> 1 or 5 is odd, a(n) = 3*n-3.

G.f.: x*(1+x+3*x^2+x^3-x^4+x^5+x^6-x^7)/((1-x)*(1-x^2)). (End)

Example

The lexicographically earliest strings of length a(n) with a minimum palindromic partition into n parts:
n | a(n) | string         | partition
--+------+----------------+---------------------------
1 | 1    | 0              | (0)
2 | 2    | 01             | (0)(1)
3 | 6    | 001011         | (0)(010)(11)
4 | 8    | 00101100       | (00)(101)(1)(00)
5 | 11   | 00101100101    | (00)(101)(1001)(0)(1)
6 | 14   | 00101110001011 | (00)(101)(11)(00)(010)(11)

Maple

f:= n -> 3*n-4+(n mod 2):
f(1):= 1: f(5):= 11:
map(f, [$1..100]); # Robert Israel, Jan 24 2018

Mathematica

With[{s = Array[Boole[# == 11] + Floor[#/6] + Floor[(# + 4)/6] + 1 &, 2^8]}, Array[FirstPosition[s, #][[1]] &, Max@ Take[#, LengthWhile[Differences@ #, # == 1 &]] &@ Union@ s]] (* Michael De Vlieger, Jan 23 2018 *)

Crossrefs

Cf. A090701, A298476.

Sequence in context: A120764 A022430 A189666 * A285971 A079418 A298170

Adjacent sequences: A298471 A298472 A298473 * A298475 A298476 A298477

Keyword

nonn

Author

Peter Kagey, Jan 19 2018

Status

approved