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%I #10 Aug 24 2015 11:33:26
%S 1,0,23,22,21,20,15,12,11,10,9,8,7,6,5,4,3,2,1,0,167,166,165,164,163,
%T 162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,
%U 145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122
%N a(n+1) = abs(a(n) - gcd(a(n), 8n+7)), a(1) = 1.
%C It is conjectured that for all n, a(n) = 0 implies that 8n+7 = a(n+1) is prime, cf. A186260. (This is the sequence {u(n)} mentioned there.)
%e a(2) = a(1) - gcd(a(1),8+7) = 1 - 1 = 0.
%e a(3) = |a(2) - gcd(a(2),8*2+7)| = gcd(0,23) = 23 (= A186260(1)) is prime.
%e a(6) = 20 and 8*6+7 = 55, thus a(7) = 20 - gcd(20,55) = 20 - 5 = 15.
%e a(8) = 15 - gcd(15,8*7+7) = 15 - 3 = 12. Note that for n = 8 + a(8) = 20, we have that 8n+7 = 167 = a(20+1) = A186260(2) is prime, while for n = 3 + a(3) = 26, 8n+7 = 215 was divisible by 5, and for n = 7 + a(7) = 22, 8n+7 = 183 was divisible by 3.
%o (PARI) print1(a=1);for(n=1,99,print1(",",a=abs(a-gcd(a,8*n+7))))
%Y Cf. A261301 - A261310, A186253 - A186263, A106108.
%K nonn
%O 1,3
%A _M. F. Hasler_, Aug 14 2015
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