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a(n) = n+1 if n+1 is a prime else a(n) = 2n+1 if 2n+1 is a prime else a(n) = 2*(2n+1) +1 =g(n) if this number is prime else the next candidate is 2*g(n) + 1 etc.
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%I #6 Dec 29 2023 13:26:21

%S 2,3,7,5,11,7,31,17,19,11,23,13,223,29,31,17,71,19,79,41,43,23,47,199,

%T 103,53,223,29,59,31,127,131,67,139,71,37,151,311,79,41,83,43,

%U 738197503,89,367,47,191,97,199,101,103,53,107,109,223,113,463,59,239,61,991,251

%N a(n) = n+1 if n+1 is a prime else a(n) = 2n+1 if 2n+1 is a prime else a(n) = 2*(2n+1) +1 =g(n) if this number is prime else the next candidate is 2*g(n) + 1 etc.

%C Subsidiary sequence: number of steps to reach a prime.

%C a(73) takes more than 2000 iterations, if it exists. - _Joshua Zucker_, May 08 2006

%e a(13) = 223, 13+1 = 14 is composite, 13*2 +1 = 27 is composite, 27*2 +1 = 55, 55*2 +1 =111 and finally 111*2 +1 = 223 is a prime.

%K easy,nonn

%O 1,1

%A _Amarnath Murthy_, Jul 23 2005

%E More terms from _Joshua Zucker_, May 08 2006