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%I #8 Apr 26 2017 15:31:17
%S 1,0,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,167,166,165,
%T 164,163,162,161,160,159,158,79,78,77,76,75,74,73,72,71,70,69,68,67,
%U 66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35
%N a(n+1) = abs(a(n) - gcd(a(n), 7*n+6)), a(1) = 1.
%C It is conjectured that for all n > 2, a(n) = 0 implies that 7n+6 = a(n+1) is prime, cf. A186259. (This is the sequence {u(n)} mentioned there.)
%H Harvey P. Dale, <a href="/A261307/b261307.txt">Table of n, a(n) for n = 1..1000</a>
%e a(2) = a(1) - gcd(a(1),7+6) = 1 - 1 = 0.
%e a(3) = |a(2) - gcd(a(2),7*2+6)| = gcd(0,17) = 17 is prime.
%e a(33) = 158, thus a(6) = 158 - gcd(158,7*33+6) = 158 - 79 = 79.
%t nxt[{n_,a_}]:={n+1,Abs[a-GCD[a,7n+6]]}; NestList[nxt,{1,1},80][[All,2]] (* _Harvey P. Dale_, Apr 26 2017 *)
%o (PARI) print1(a=1);for(n=1,99,print1(",",a=abs(a-gcd(a,7*n+6))))
%Y Cf. A261301 - A261310, A186253 - A186263, A106108.
%K nonn
%O 1,3
%A _M. F. Hasler_, Aug 14 2015
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