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Smallest prime factor of f(n) = 10^(2*n) + (10^n - 1)/9.
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%I #59 Oct 22 2023 06:45:10

%S 101,3,7,7,3,317,40637,3,7,7,3,1487,101,3,7,7,3,39855301,641,3,7,7,3,

%T 162340676822011484150719,101,3,7,7,3,121068683,47,3,7,7,3,107,71,3,7,

%U 7,3,67,695841737,3,7,7,3,47,101,3,7,7,3,8933,677,3,7,7,3,10305833206337

%N Smallest prime factor of f(n) = 10^(2*n) + (10^n - 1)/9.

%F a(3k + 2) = 3, a(6k + 3) = 7, a(6k + 4) = 7.

%e a(1) = 101, because f(1) = 101 is prime.

%e a(2) = 3, because the smallest prime factor of f(2) = 10011 = 3 * 337 is 3.

%t a[n_]:=Min[First/@FactorInteger[10^(2*n)+(10^n-1)/9]]; Array[a,59] (* _Stefano Spezia_, Sep 24 2023 *)

%o (PARI) a(n)=my(x=10^(2*n)+(10^n-1)/9);m=factor(x);return(m[1,1])

%o (PARI) a(n) = my(x=10^(2*n)+(10^n-1)/9, k=10); if (ispseudoprime(x), return(x)); while (1, m=factor(x, k); if (m[1,1]<x, return(m[1,1])); k*=10); \\ _Michel Marcus_, Sep 24 2023

%Y Cf. A020639, A067063, A365966, A102380.

%K nonn

%O 1,1

%A _Jean-Marc Rebert_, Sep 23 2023

%E a(60) from _Jinyuan Wang_, Sep 24 2023