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 A082983 Odd numbers which lead to 1 in the 3x+1 problem, generated by a particular "least-first" greedy algorithm (see program code). 0
 1, 5, 3, 13, 17, 11, 7, 9, 21, 29, 19, 25, 33, 37, 45, 49, 53, 35, 23, 15, 61, 65, 43, 57, 69, 77, 51, 81, 85, 93, 101, 67, 89, 59, 39, 113, 75, 117, 133, 141, 149, 99, 157, 173, 115, 153, 177, 181, 197, 131, 87, 205, 209, 139, 185, 123, 213, 229, 237, 241, 245, 163, 217 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS It is suspected but not proved that all odd integers are in the sequence - this is equivalent to whether all numbers reach 1 in the 3x+1 problem. The program code given below does not actually represent infinite sets, but the result is the same since the smallest remaining member of each sibling-set is always present. LINKS EXAMPLE The second term is 5 because if we take 1 (our starting point), create all powers of twice it and subtract 1 and divide by 3 for those which will give an integer result, we get the set {5,21,85,...} (sequence A002450) and 5 is the smallest member of that set. The next term is 3 because we generate all of 5's children {3,13,53,213,...} (sequence A072197) and merge that with the set leftover from before (5's siblings {21,85,...}) and the smallest member is 3. 3 has no children, so the next term is 13. PROG #!/usr/bin/perl @list = ( 1 ); while (1) { \$n = shift @list; print "\$n "; # next sibling push(@list, 4*\$n + 1); # first child if ((\$n % 3) == 1) { \$n = (\$n*4 - 1)/3; while (\$n && ((\$n % 2) == 0)) { \$n /= 2; } push(@list, \$n) unless (\$n <= 1); } elsif ((\$n % 3) == 2) { \$n = (\$n*2 - 1)/3; while (\$n && ((\$n % 2) == 0)) { \$n /= 2; } push(@list, \$n) unless (\$n <= 1); } #else do nothing, since == 0 mod 3 has no children # Inefficient - should have heap insertion sort. @list = sort numeric @list; } sub numeric { \$a <=> \$b; } CROSSREFS Cf. A002450, A072197. Sequence in context: A080797 A085910 A093544 * A083594 A178497 A213750 Adjacent sequences:  A082980 A082981 A082982 * A082984 A082985 A082986 KEYWORD easy,nonn AUTHOR Howard A. Landman (howard(AT)riverrock.org), May 28 2003 STATUS approved

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Last modified May 24 05:45 EDT 2013. Contains 225617 sequences.