This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A341115 #17 Mar 28 2021 15:54:24 %S A341115 125000,61298400,578869250,4511718750,195312500000,2918554687500, %T A341115 3874552343750 %N A341115 Numbers k such that k*2^101 + 1 is a prime factor of 10^(10^100) + 1. %C A341115 Every prime factor of 10^(10^100) + 1 is of the given form (k == 1 (mod 2^101)). %C A341115 If k is not divisible by 10, then k == 1,3,4 (mod 10), and k*2^101 + 1 divides 10^(2^100) + 1. %C A341115 If 1 <= j <= 99 and k is not divisible by 5^(j+1), then k*2^101 + 1 divides 10^(2^100*5^j) + 1. %C A341115 No other terms below 4*10^12. Other known terms in this sequence are 397299146187500, 194585800170898437500, 3163315773010253906250, 3274180926382541656494140625000, 128238752949982881546020507812500, 13940493204245285596698522567749023437500, 61902333925445418572053313255310058593750, 146251500493521646717454132158309221267700195312500. %H A341115 D. A. Alpern, <a href="https://www.alpertron.com.ar/GOOGOL.HTM">Factors of 1000 numbers starting from googolplex</a> %e A341115 The smallest prime factor of 10^10^100 + 1 is 125000*2^100 + 1 = 316912650057057350374175801344000001. %o A341115 (Python) %o A341115 A341115_list, k, m, l, n = [], 1, 2**101, 2**101+1, 10**100 %o A341115 while k < 10**6: %o A341115 if pow(10,n,l) == l-1: %o A341115 A341115_list.append(k) %o A341115 print(len(A341115_list),k) %o A341115 k += 1 %o A341115 l += m # _Chai Wah Wu_, Mar 28 2021 %Y A341115 Cf. A341116 (corresponding primes), A072288. %K A341115 nonn,fini,hard,more %O A341115 1,1 %A A341115 _Yan Sheng Ang_, Feb 05 2021