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A127597 Least number k such that k 4^n + (4^n-1)/3 is prime.

%I A127597 #12 May 19 2022 17:43:31
%S A127597 2,1,0,2,3,2,4,4,3,10,3,3,2,7,2,25,6,17,4,13,3,20,36,20,11,27,66,23,
%T A127597 39,24,19,13,3,10,6,122,71,58,24,13,3,2,41,10,6,32,58,17,4,79,26,55,
%U A127597 36,48,31,28,9,2,76,24,32,28,63,20,37,9,2,7,39,10,91,47
%N A127597 Least number k such that k 4^n + (4^n-1)/3 is prime.
%H A127597 Michael S. Branicky, <a href="/A127597/b127597.txt">Table of n, a(n) for n = 0..2391</a>
%t A127597 a = {}; Do[k = 0; While[ !PrimeQ[k 4^n + (4^n - 1)/3], k++ ]; AppendTo[a, k], {n, 0, 50}]; a (*Artur Jasinski*)
%t A127597 lnk[n_]:=Module[{k=0,n4=4^n},While[!PrimeQ[k*n4+(n4-1)/3],k++];k]; Array[ lnk,60,0] (* _Harvey P. Dale_, May 28 2018 *)
%o A127597 (Python)
%o A127597 from sympy import isprime
%o A127597 def a(n):
%o A127597     k, fourn = 0, 4**n
%o A127597     while not isprime(k*fourn + (fourn-1)//3): k += 1
%o A127597     return k
%o A127597 print([a(n) for n in range(72)]) # _Michael S. Branicky_, May 18 2022
%Y A127597 Cf. A035050, A007522, A127575, A127576, A127577, A127578, A127580, A127581, A087522, A127586, A127587, A127589, A127590, A127591, A127592, A127593, A127594, A127598.
%K A127597 nonn
%O A127597 0,1
%A A127597 _Artur Jasinski_, Jan 19 2007
%E A127597 Offset corrected and a(51) and beyond from _Michael S. Branicky_, May 18 2022