

A141447


Set m_0=0, and let m_n be the least positive integer that cannot be written in the form Sum_{k=1..oo} a_k k!, with a_k in {m_0,m_1, ..., m_{n1}}.


0



0, 1, 4, 5, 22, 23, 82, 83, 466, 467, 478, 479, 1090486, 1090487, 1090774, 1090775, 1090846, 1090847
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,3


COMMENTS

This sequence was suggested by Kevin O'Bryant, who provided terms a(0)a(11); a(12)a(17) were from David S. Newman.
The numbers always come in pairs, the first even, then the following odd number.
The next number in the sequence exceeds 3*10^6.


LINKS

Table of n, a(n) for n=0..17.


EXAMPLE

Example: When m_0=0 and m_1=1, the numbers from 1 to 3 may be written 1=1*1!, 2=1*2!, 3= 1*1! + 1*2!, but there is no way to write 4. So m_2 is taken to be 4.


MATHEMATICA

(* These values can be found by entering m={0, 1} separately and then iterating the following program: *)
searchbound=2 10^6;
poly=Expand[Total[qSelect[m, EvenQ]]Product[Total[qSelect[#*n!&/@m, #searchbound&]], {n, 2, 10}]];
i=1; found=False;
While[foundFalse&&i<2000000, i=i+1;
If[Coefficient[poly[[i+1]], q, 2i]0, found=True; AppendTo[m, 2i]; AppendTo[m, 2i+1]; Print["m= ", m]]]
(* Please note: I copied and pasted this program, but it has printed on this screen differently from the way it did in the Mathematica environment. If it does not run as is, I can send the Mathematica file to anyone who wants it. *)


CROSSREFS

Sequence in context: A178625 A284911 A091130 * A129346 A291670 A176957
Adjacent sequences: A141444 A141445 A141446 * A141448 A141449 A141450


KEYWORD

nonn


AUTHOR

David S. Newman, Dec 16 2010


STATUS

approved



