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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_{n-1}}. 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)



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.


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


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.


(* 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[foundFalse&&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. *)


Sequence in context: A178625 A284911 A091130 * A129346 A291670 A176957

Adjacent sequences:  A141444 A141445 A141446 * A141448 A141449 A141450




David S. Newman, Dec 16 2010



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Last modified April 14 21:21 EDT 2021. Contains 342962 sequences. (Running on oeis4.)