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.

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, 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, 5, 0, 0, 1, 6, 4, 3, 0, 0, 1, 2, 0, 3, 2, 0, 1, 0, 2, 7

Offset: 1

Author

Felix Fröhlich, Jun 24 2021

Keywords

• sign

Comments

a(159986/2) = a(79993) = -1.

Examples

			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.
		

Links

• Joe O, Project Description, Mersenne forum.
• Reggie, Welcome to the Sierpinski/Riesel Base 5 Project, PrimeGrid forum.
• Wikipedia, Sierpiński number

Crossrefs

Cf. A123159, A291437 (Sierpiński problem base 3), A345403 (Riesel problem base 5).

Programs

PARI

a(n) = for(k=0, oo, if(ispseudoprime((2*n)*5^k+1), return(k)))