A362429 -id:A362429 - cp's OEIS frontend

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

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

Offset: 1

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

nonn

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

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

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

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

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

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

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

A376221 The smallest Champernowne prime in base n.

Original entry on oeis.org

3, 5, 109, 7, 18796638871, 131870666077, 83, 11, 1234567891, 13, 24677

Offset: 2

Scott R. Shannon, Sep 16 2024

See A176942 for further details.
If a(13) exists it has more than 4800 decimal digits. See the attached text file for other known values up to n = 36.
If a(13) exists it has more than 86468 decimal digits, corresponding to concatenation of up to 20000 base-13 numbers. - Michael S. Branicky, Sep 20 2024

			a(2) = 3 as 11_2 is prime.
a(3) = 5 as 12_3 is prime.
a(4) = 109 as 1231_4 is prime.
a(5) = 7 as 12_5 is prime.
a(6) = 18796638871 as 12345101112131_6 is prime.
a(7) = 131870666077 as 12345610111213_7 is prime.
a(8) = 83 as 123_8 is prime.
a(9) = 11 as 12_9 is prime.
a(10) = 1234567891 as 1234567891_10 is prime. See A176942.
a(11) = 13 as 12_11 is prime.
a(12) = 24677 as 12345_12 is prime.

Scott R. Shannon, a(n) for n = 2..36. A value of -1 indicates the term is currently unknown.

Cf. A176942, A073175, A114754, A000040, A362429.

cp's OEIS Frontend

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

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