A362118 a(n) = (10^(n*(n+1)/2)-1)/9.

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]

Links

Table of n, a(n) for n=1..11.

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

Cf. A000042, A004023, A058935, A360502, A117640, A007908.

Sequence in context: A362920 A244845 A152775 * A242646 A242645 A262647

Adjacent sequences: A362115 A362116 A362117 * A362119 A362120 A362121

Keyword

nonn

Author

Michael S. Branicky and N. J. A. Sloane, Apr 19 2023

Status

approved