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 A362118 #30 Apr 18 2025 21:26:21 %S A362118 1,111,111111,1111111111,111111111111111,111111111111111111111, %T A362118 1111111111111111111111111111,111111111111111111111111111111111111, %U A362118 111111111111111111111111111111111111111111111,1111111111111111111111111111111111111111111111111111111,111111111111111111111111111111111111111111111111111111111111111111 %N A362118 a(n) = (10^(n*(n+1)/2)-1)/9. %C A362118 Concatenate 1, 11, 111, ..., 11...1 (n ones). There are n*(n+1)/2 1's in a(n). %C A362118 This is a kind of unary analog of A058935, A360502, A117640, etc. %C A362118 When regarded as decimal numbers, which (if any) is the smallest prime? %C A362118 Answer: All terms > 1 are composite, since 111 is composite, all triangular numbers > 3 are composite and a prime repunit must have a prime number of decimal digits (see A004023). - _Chai Wah Wu_, Apr 19 2023. [This result was independently obtained by _Michael S. Branicky_, see A362429. - _N. J. A. Sloane_, Apr 20 2023] %C A362118 a(45) has more than 1000 digits, and so cannot be included in the b-file. - _Jason Bard_, Apr 12 2025 %H A362118 Jason Bard, <a href="/A362118/b362118.txt">Table of n, a(n) for n = 1..44</a> %F A362118 a(n) = A000042(A000217(n)). - _Jason Bard_, Apr 12 2025 %e A362118 a(3) = 111111 because 3(3+1)/2 = 6, and 111111 has 6 ones. %t A362118 A362118[n_]:=(10^(n(n+1)/2)-1)/9;Array[A362118,10] (* _Paolo Xausa_, Nov 27 2023 *) %o A362118 (Python) %o A362118 def A362118(n): return 10**(n*(n+1)>>1)//9 # _Chai Wah Wu_, Apr 19 2023 %Y A362118 Cf. A000042, A004023, A058935, A360502, A117640, A007908. %K A362118 nonn %O A362118 1,2 %A A362118 _Michael S. Branicky_ and _N. J. A. Sloane_, Apr 19 2023