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%I #24 Nov 27 2023 14:46:55
%S 1,111,111111,1111111111,111111111111111,111111111111111111111,
%T 1111111111111111111111111111,111111111111111111111111111111111111,
%U 111111111111111111111111111111111111111111111,1111111111111111111111111111111111111111111111111111111,111111111111111111111111111111111111111111111111111111111111111111
%N a(n) = (10^(n*(n+1)/2)-1)/9.
%C Concatenate 1, 11, 111, ..., 11...1 (n ones). There are n*(n+1)/2 1's in a(n).
%C This is a kind of unary analog of A058935, A360502, A117640, etc.
%C When regarded as decimal numbers, which (if any) is the smallest prime?
%C 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]
%t A362118[n_]:=(10^(n(n+1)/2)-1)/9;Array[A362118,10] (* _Paolo Xausa_, Nov 27 2023 *)
%o (Python)
%o def A362118(n): return 10**(n*(n+1)>>1)//9 # _Chai Wah Wu_, Apr 19 2023
%Y Cf. A000042, A004023, A058935, A360502, A117640, A007908.
%K nonn
%O 1,2
%A _Michael S. Branicky_ and _N. J. A. Sloane_, Apr 19 2023