A385331 a(1) = 1 and a(n) is the smallest prime factor of n-th numerator of partial sum for Liouville's constant (A145571), for n > 1.

1, 11, 3, 4447, 7823, 3, 7, 13, 3, 61, 31, 3, 11, 7, 3, 9281, 19163, 3, 17, 53861, 3, 599, 397, 3

Offset: 1

Author

Gonzalo Martínez, Jun 25 2025

Keywords

• nonn
• base
• more

Comments

a(n) = A145571(n) itself when that numerator is prime: are there any others after a(2) = 11?

Examples

			For n=3, the prime decomposition A145571(3) = 110001 = 3*37*991 so that a(3) = 3.
		

Crossrefs

Cf. A012245, A145571.

Programs

PARI

a(n) = if(n>1, forprime(p=3, oo, if(sum(k=1, n, Mod(10, p)^(n!-k!))==0, return(p))), 1); \\ Jinyuan Wang, Jun 25 2025

Formula

a(3k) = 3 for k >= 1, since A145571(n) is an odd number whose sum of digits is n so at n = 3k it is divisible by 3.

Extensions

a(10)-a(24) from Jinyuan Wang, Jun 25 2025