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A345698 Sierpiński problem in base 5: a(n) is the smallest k >= 0 such that (2*n)*5^k + 1 is prime, or -1 if no such k exists.

%I A345698 #8 Jul 01 2021 15:51:33
%S A345698 0,0,0,1,0,0,1,0,0,1,0,2,1,0,0,3,8,0,1,0,0,3,0,1,1,0,1,1,0,0,1,2,0,3,
%T A345698 0,0,257,2,0,1,0,1,1,0,2,1,2,0,1,0,0,1,0,0,3,0,1,15,4,1,79,48,0,1,0,1,
%U A345698 5,0,0,1,6,4,3,0,0,1,2,0,3,2,0,1,0,2,7
%N A345698 Sierpiński problem in base 5: a(n) is the smallest k >= 0 such that (2*n)*5^k + 1 is prime, or -1 if no such k exists.
%C A345698 a(159986/2) = a(79993) = -1.
%H A345698 Joe O, <a href="https://www.mersenneforum.org/showpost.php?p=233495&amp;postcount=1">Project Description</a>, Mersenne forum.
%H A345698 Reggie, <a href="https://www.primegrid.com/forum_thread.php?id=5087&amp;nowrap=true#66386">Welcome to the Sierpinski/Riesel Base 5 Project</a>, PrimeGrid forum.
%H A345698 Wikipedia, <a href="https://en.wikipedia.org/wiki/Sierpi%C5%84ski_number">Sierpiński number</a>
%e A345698 For n = 17: 34*5^k + 1 is composite for k = 0, 1, 2, 3, 4, 5, 6, 7 and prime for k = 8. Since 8 is the smallest such k, a(17) = 8.
%o A345698 (PARI) a(n) = for(k=0, oo, if(ispseudoprime((2*n)*5^k+1), return(k)))
%Y A345698 Cf. A123159, A291437 (Sierpiński problem base 3), A345403 (Riesel problem base 5).
%K A345698 sign
%O A345698 1,12
%A A345698 _Felix Fröhlich_, Jun 24 2021