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

1, 111, 111111, 1111111111, 111111111111111, 111111111111111111111, 1111111111111111111111111111, 111111111111111111111111111111111111, 111111111111111111111111111111111111111111111, 1111111111111111111111111111111111111111111111111111111, 111111111111111111111111111111111111111111111111111111111111111111

Offset: 1

Author

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

Keywords

• nonn

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]

a(45) has more than 1000 digits, and so cannot be included in the b-file. - Jason Bard, Apr 12 2025

Examples

			a(3) = 111111 because 3(3+1)/2 = 6, and 111111 has 6 ones.
		

Links

• Jason Bard, Table of n, a(n) for n = 1..44

Crossrefs

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

Programs

Mathematica

A362118[n_]:=(10^(n(n+1)/2)-1)/9;Array[A362118,10] (* Paolo Xausa, Nov 27 2023 *)

Python

def A362118(n): return 10**(n*(n+1)>>1)//9 # Chai Wah Wu, Apr 19 2023

Formula

a(n) = A000042(A000217(n)). - Jason Bard, Apr 12 2025