A276786 - OEIS

%I #31 Oct 20 2019 21:59:39

%S 1,3,4,7,9,10,13,15,19,21,22,27,28,31,31,39,40,43,45,46,55,57,58,63,

%T 63,64,67,79,81,82,85,87,91,93,94,94,111,115,117,118,121,127,127,129,

%U 130,135,136,139,159,163,165,166,171,172,175,175,183,187,189,189,190,190,193,202,223,231,235,237,238

%N a(1) = 1; subsequent terms are defined by the rule that if m is present so are 2m+1 and 3m+1; repeated terms are included; final list is sorted.

%C 31 is the first number to appear twice. This is a multi-set version of the Klarner-Rado sequence A002977.

%C 20479 is the first number to appear three times. - _Rémy Sigrist_, Dec 19 2016

%H Rémy Sigrist, <a href="/A276786/b276786.txt">Table of n, a(n) for n = 1..29993</a> [Terms up to 500000]

%H J. C. Lagarias, <a href="http://www.jstor.org/stable/10.4169/amer.math.monthly.123.8.753">Erdős, Klarner and the 3x + 1 Problem</a>, Amer. Math. Monthly 123 (No. 8, 2016), 753-776. See S# on page 756.

%H Rémy Sigrist, <a href="/A276786/a276786.c++.txt">C99 program for A276786</a>

%p KR:=proc(lis) local i,j,t1,t2,t3;

%p t1:=lis; t2:=nops(lis); t3:=[];

%p for i from 1 to t2 do j:=t1[i];

%p t3:=[op(t3),2*j+1,3*j+1]; od: sort(t3); end;

%p t:=[1]; b:=[1];

%p for n from 1 to 10 do

%p t:=KR(t); b:=[op(b),op(t)]; b:=sort(b);

%p od: b;

%Y Cf. A002977. See A276787 for repeated terms.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Oct 06 2016