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A362118
a(n) = (10^(n*(n+1)/2)-1)/9.
4
1, 111, 111111, 1111111111, 111111111111111, 111111111111111111111, 1111111111111111111111111111, 111111111111111111111111111111111111, 111111111111111111111111111111111111111111111, 1111111111111111111111111111111111111111111111111111111, 111111111111111111111111111111111111111111111111111111111111111111
OFFSET
1,2
COMMENTS
Concatenate 1, 11, 111, ..., 11...1 (n ones). There are n*(n+1)/2 1's in a(n).
This is a kind of unary analog of A058935, A360502, A117640, etc.
When regarded as decimal numbers, which (if any) is the smallest prime?
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]
MATHEMATICA
A362118[n_]:=(10^(n(n+1)/2)-1)/9; Array[A362118, 10] (* Paolo Xausa, Nov 27 2023 *)
PROG
(Python)
def A362118(n): return 10**(n*(n+1)>>1)//9 # Chai Wah Wu, Apr 19 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved