A323060 - OEIS

%I #51 Feb 28 2020 00:03:53

%S 1,91,8190090090909099099181

%N 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.

%C a(4) has 196 digits.

%C 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.

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

%H Michel Marcus, <a href="/A323060/b323060.txt">Table of n, a(n) for n = 1..4</a>

%H Patrick A. Thomas, <a href="/A323060/a323060_3.txt">Term a(5) and information on a(6)</a>

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

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

%o (PARI) R(n) = (10^n-1)/9; \\ A002275

%o primo(n) = prod(i=1, n, prime(i)); \\ A002110

%o a(n) = R(primo(n))/prod(j=1, n, R(prime(j))); \\ _Michel Marcus_, Jan 21 2019

%Y Cf. A002110, A002275, A031974.

%K nonn,easy

%O 1,2

%A _Patrick A. Thomas_, Jan 19 2019