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a(n) = A085956(3n+1).
5

%I #8 May 15 2017 23:37:58

%S 5,17,239,41,131,1889,419,89,101,113,2543,2789,149,881,173,9293,491,

%T 14249,3191,1973,3539,21377,7103,281,5987,38153,317,2789,6971,353,

%U 214943,42677,3299,11801,2267,27773,29867,10529,461,1181,2663,129209

%N a(n) = A085956(3n+1).

%C A086361 and A086362 includes most probably the solvable [or small?] cases of A085956, where n=3k-1 has probably only two solutions, at [k,n,a(n)]=[1,2,13] and at [2,5,31].

%H Michael De Vlieger, <a href="/A086362/b086362.txt">Table of n, a(n) for n = 0..1000</a>

%e n=50:3n+1=151,6n+2=302, a(50)=93923 prime with (93922-1)/302=311, prime and with 302.93923+1=28364747 prime; so the {311,93923,28364747} "generalized [short] Cunningham-chain" is defined.

%t Table[Function[m, p = 2; While[Nand @@ PrimeQ@ {2 m p + 1, (p - 1)/(2 m)}, p = NextPrime@ p]; p][3 n + 1], {n, 0, 41}] (* _Michael De Vlieger_, May 15 2017 *)

%Y Cf. A085956, A086361.

%K nonn

%O 0,1

%A _Labos Elemer_, Jul 22 2003