%I A084663
%S A084663 8,10,11,12,13,14,21,22,23,24,25,26,39,40,45,46,47,48,49,50,51,52,53,54,
%T A084663 55,56,57,58,87,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,
               106,
%U A084663 107,108,109,110,111,112,113,114,115,116,117,118,177,180,181,182,189,190
%N A084663 a(1) = 8; a(n) = a(n-1) + gcd(a(n-1), n).
%C A084663 The first 150000000 differences are all primes or 1. Is this true in 
               general?
%D A084663 Eric S. Rowland, A simple prime-generating recurrence, Abstracts Amer. 
               Math. Soc., 29 (No. 1, 2008), p. 50 (Abstract 1035-11-986).
%H A084663 T. D. Noe, <a href="b084663.txt">Table of n, a(n) for n=1..1000</a>
%H A084663 Eric S. Rowland, <a href="http://arXiv.org/abs/0710.3217">A simple prime-generating 
               recurrence</a>.
%p A084663 S := 8; f := proc(n) option remember; global S; if n=1 then S else f(n-1)+igcd(n,
               f(n-1)); fi; end;
%t A084663 f[n_] := f[n-1] + GCD[n, f[n-1]]; f[1]=8
%Y A084663 Cf. A084662, A106108.
%Y A084663 Sequence in context: A031953 A043697 A043425 this_sequence A031037 A006757 
               A126803
%Y A084663 Adjacent sequences: A084660 A084661 A084662 this_sequence A084664 A084665 
               A084666
%K A084663 nonn
%O A084663 1,1
%A A084663 Matthew Frank (mfrank(AT)wopr.wolfram.com) on behalf of the 2003 New 
               Kind of Science Summer School, Jul 15 2003