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A185069 Primes of the form k*6^m +1 with k prime and m an integer.

%I A185069 #41 Feb 20 2023 07:51:47
%S A185069 3,13,19,31,43,67,73,79,103,109,139,181,223,283,367,397,433,439,499,
%T A185069 607,613,619,643,787,823,829,907,1039,1087,1117,1399,1447,1543,1549,
%U A185069 1579,1627,1663,1693,1699,1759,1867,1879,1987,2083,2203,2239,2377
%N A185069 Primes of the form k*6^m +1 with k prime and m an integer.
%C A185069 Companion sequence to A186782.
%H A185069 Harvey P. Dale, <a href="/A185069/b185069.txt">Table of n, a(n) for n = 1..1000</a>
%e A185069 5*6^1+1 = 31 is prime and therefore a term.
%e A185069 7*6^2+1 = 253 is composite and therefore not in the sequence.
%e A185069 17*6^13+1 = 222031798273 is prime and therefore a term (see also its companion in A186782).
%t A185069 Module[{upto=3000,pr},pr=PrimePi[upto]+1;Select[Sort[Flatten[ Table[ k*6^m+1,{k,Prime[Range[pr]]},{m,0,Log[6,(upto-1)/6]}]]],PrimeQ[#] && 185#<=upto&]](* _Harvey P. Dale_, Dec 30 2018 *)
%o A185069 (Sage)
%o A185069 def is_A185069(n):
%o A185069     k = n - 1
%o A185069     while k % 6 == 0: k //= 6
%o A185069     return is_prime(k)
%o A185069 A185069_list = [p for p in primes(3000) if is_A185069(p)] # _D. S. McNeil_, Feb 20 2011
%o A185069 (Magma) IsA185069:=function(n); k:=n-1; while k mod 6 eq 0 do k:=(k div 6); end while; return IsPrime(k); end function; [ n: n in PrimesUpTo(3000) | IsA185069(n) ];
%Y A185069 Cf. A186104, A186105, A185167, A186782.
%K A185069 nonn
%O A185069 1,1
%A A185069 _Gilbert Mozzo_, Feb 18 2011
%E A185069 Edited by _N. J. A. Sloane_, Feb 20 2011