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A076034 Group the natural numbers so that the n-th group contains the smallest set of n relatively prime numbers: (1), (2, 3), (4, 5, 7), (6, 11, 13, 17), (8, 9, 19, 23, 25), (10, 21, 29, 31, 37, 41), ...

%I A076034 #23 Oct 04 2024 10:00:04
%S A076034 1,2,3,4,5,7,6,11,13,17,8,9,19,23,25,10,21,29,31,37,41,12,35,43,47,53,
%T A076034 59,61,14,15,67,71,73,79,83,89,16,27,49,55,97,101,103,107,109,18,65,
%U A076034 77,113,127,131,137,139,149,151,20,33,91,157,163,167,173,179,181,191,193
%N A076034 Group the natural numbers so that the n-th group contains the smallest set of n relatively prime numbers: (1), (2, 3), (4, 5, 7), (6, 11, 13, 17), (8, 9, 19, 23, 25), (10, 21, 29, 31, 37, 41), ...
%H A076034 Paul Tek, <a href="/A076034/b076034.txt">Table of n, a(n) for n = 1..10000</a>
%H A076034 Paul Tek, <a href="/A076034/a076034.pl.txt">PERL program for this sequence</a>
%e A076034 The triangle begins:
%e A076034    1;
%e A076034    2, 3;
%e A076034    4,  5,  7;
%e A076034    6, 11, 13, 17;
%e A076034    8,  9, 19, 23, 25;
%e A076034   10, 21, 29, 31, 37, 41;
%e A076034   ...
%p A076034 S:=[$1..1000]: Res:= NULL:
%p A076034 for n from 1 to 20 do
%p A076034   A:= [S[1]]; R:= 1; count:= 1;
%p A076034   for k from 2 while count < n do
%p A076034     if andmap(t -> igcd(t,S[k])=1, A) then count:= count+1; A:= [op(A),S[k]]; R:= R,k; fi
%p A076034   od;
%p A076034   S:= subsop(op(map(t -> t=NULL, [R])),S);
%p A076034   Res:= Res, op(A);
%p A076034 od:
%p A076034 Res; # _Robert Israel_, Dec 04 2022
%o A076034 (Perl) # See Links section.
%Y A076034 Cf. A075383, A076032, A076033, A095167.
%K A076034 nonn,tabl,look
%O A076034 1,2
%A A076034 _Amarnath Murthy_, Oct 01 2002
%E A076034 More terms from _David Wasserman_, Jan 29 2005
%E A076034 Crossrefs added by _Paul Tek_, Oct 24 2015