A323060 a(n) = R_(prime(n)#) / Product_{j=1..n} R_(prime(j)), where prime(n)# is the n-th primorial number A002110(n) and R_k = (10^k - 1)/9.

1, 91, 8190090090909099099181

Offset: 1

Author

Patrick A. Thomas, Jan 19 2019

Keywords

• nonn
• easy

Comments

a(4) has 196 digits.

The numbers R_k = 1, 11, 111, ... are sometimes called "Rep-units" or "repunits". The octal versions of a(1) through a(4) may be obtained from the decimal versions by replacing each 6 with a 4, each 7 with a 5, each 8 with a 6, and each 9 with a 7. Similar relations exist for other bases.

Examples

			R_30 / (11*111*11111) = 8190090090909099099181.
		

References

• Author?, "The Ultimate Number Series Challenge", Vidya, Oct 1988, p. 9.

Links

• Michel Marcus, Table of n, a(n) for n = 1..4
• Patrick A. Thomas, Term a(5) and information on a(6)

Crossrefs

Cf. A002110, A002275, A031974.

Programs

Mathematica

f[n_] := (10^n - 1)/9; Array[f[Product[Prime@ i, {i, #}]]/Product[f@ Prime@ j, {j, #}] &, 3] (* Michael De Vlieger, Jan 19 2019 *)

PARI

R(n) = (10^n-1)/9; \\ A002275
primo(n) = prod(i=1, n, prime(i)); \\ A002110
a(n) = R(primo(n))/prod(j=1, n, R(prime(j))); \\ Michel Marcus, Jan 21 2019