A298476 Least k such that A298475(k) = n.

1, 2, 37, 203, 1332, 13428, 160884, 858740, 10295924, 54958708, 658938484, 3517356660

Offset

1,2

Comments

A298474(n) = floor(log_2(a(n))) + 1.

Links

Table of n, a(n) for n=1..12.

Rémy Sigrist, C program for A298476

Formula

a(n) >= 2^(A298474(n) - 1).

a(n) < 2^A298474(n).

Example

The smallest partition of the binary representation of A298476(k) is:
k | A298476(k) |               partition
--+------------+---------------------------------------
1 |        1   |                                  (1)_2
2 |        2   |                               (1)(0)_2
3 |       37   |                         (1001)(0)(1)_2
4 |      203   |                     (11)(00)(101)(1)_2
5 |     1332   |                (101)(00)(1)(101)(00)_2
6 |    13428   |           (11)(010)(0)(01110)(1)(00)_2
7 |   160884   |     (1001)(1)(101)(000)(111)(010)(0)_2
8 |   858740   | (11)(010)(0)(0110)(1001)(11)(010)(0)_2

Mathematica

With[{s = {1, 2}~Join~Array[Function[w, Min@ Map[Length, Select[#, And[AllTrue[#, PalindromeQ], Union@ Map[Length, #] != {1}] &]] &@ Union@ Map[Select[SplitBy[#, IntegerQ], IntegerQ@ First@ # &] &, Map[Insert[w, ".", #] &, Map[{#} &, Rest@ Subsets@ Range@ Length@ w, {2}]]]]@ IntegerDigits[#, 2] &, 1400, 3]}, Array[FirstPosition[s, #][[1]] &, Max@ Take[#, 1 + LengthWhile[Differences@ #, # == 1 &]] &@ Union@ s]] (* Michael De Vlieger, Jan 23 2018 *)

Prog

(C) See Links section.

Crossrefs

Cf. A298474, A298475.

Sequence in context: A134596 A139119 A244757 * A302883 A053788 A078976

Adjacent sequences: A298473 A298474 A298475 * A298477 A298478 A298479

Keyword

nonn,base,more

Author

Peter Kagey, Jan 19 2018

Extensions

a(9)-a(12) from Rémy Sigrist, Dec 28 2019

Status

approved