A276786 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.

1, 3, 4, 7, 9, 10, 13, 15, 19, 21, 22, 27, 28, 31, 31, 39, 40, 43, 45, 46, 55, 57, 58, 63, 63, 64, 67, 79, 81, 82, 85, 87, 91, 93, 94, 94, 111, 115, 117, 118, 121, 127, 127, 129, 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

Offset

1,2

Comments

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

20479 is the first number to appear three times. - Rémy Sigrist, Dec 19 2016

Links

Rémy Sigrist, Table of n, a(n) for n = 1..29993 [Terms up to 500000]

J. C. Lagarias, Erdős, Klarner and the 3x + 1 Problem, Amer. Math. Monthly 123 (No. 8, 2016), 753-776. See S# on page 756.

Rémy Sigrist, C99 program for A276786

Maple

KR:=proc(lis) local i, j, t1, t2, t3;
t1:=lis; t2:=nops(lis); t3:=[];
for i from 1 to t2 do j:=t1[i];
t3:=[op(t3), 2*j+1, 3*j+1]; od: sort(t3); end;
t:=[1]; b:=[1];
for n from 1 to 10 do
t:=KR(t); b:=[op(b), op(t)]; b:=sort(b);
od: b;

Crossrefs

Cf. A002977. See A276787 for repeated terms.

Sequence in context: A029739 A005098 A185661 * A002977 A024799 A240531

Adjacent sequences: A276783 A276784 A276785 * A276787 A276788 A276789

Keyword

nonn

Author

N. J. A. Sloane, Oct 06 2016

Status

approved