1,2

David Klarner and coauthors studied several sequences of this type. Some of the references here apply generally to this class of sequences.

R. K. Guy, Don't try to solve these problems, Amer. Math. Monthly, 90 (1983), 35-41.

Guy, R. K., Klarner-Rado Sequences. Section E36 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 237, 1994.

Hoffman, D. G. and Klarner, D. A. Sets of integers closed under affine operators-the finite basis theorem. Pacific J. Math. 83 (1979), no. 1, 135-144.

Hoffman, D. G. and Klarner, D. A. Sets of integers closed under affine operators-the closure of finite sets. Pacific J. Math. 78 (1978), no. 2, 337-344.

Klarner, David A., m-Recognizability of sets closed under certain affine functions. Discrete Appl. Math. 21 (1988), no. 3, 207-214.

Klarner, David A. and Post, Karel Some fascinating integer sequences. A collection of contributions in honour of Jack van Lint. Discrete Math. 106/107 (1992), 303-309.

Klarner, D. A. and Rado, R. Arithmetic properties of certain recursively defined sets. Pacific J. Math. 53 (1974), 445-463.

R. J. Mathar, Table of n, a(n) for n = 1..15889

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

(C++) #include <stdio.h> #include <iostream> #include <set> using namespace std ; int main(int argc, char *argv[]) { const int anmax= 40000 ; set<int> a ; a.insert(1) ; for(int i=0; i< anmax ; i++) { if( a.count(i) ) { if( 2*i<=anmax) a.insert(2*i) ; if( 3*i+2 <= anmax) a.insert(3*i+2) ; if( 6*i+3 <= anmax) a.insert(6*i+3) ; } } int n=1 ; for(int i=0; i < anmax; i++) { if( a.count(i) ) { cout << n << " " << i << endl ; n++ ; } } return 0 ; } - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 20 2006

Sequence in context: A069011 A101185 A045702 this_sequence A003714 A010402 A010443

Adjacent sequences: A005655 A005656 A005657 this_sequence A005659 A005660 A005661

nonn,easy,nice

njas

More terms from Larry Reeves (larryr(AT)acm.org), Oct 16 2000