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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. 2
1, 91, 8190090090909099099181 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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.

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)

EXAMPLE

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

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 *)

PROG

(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

CROSSREFS

Cf. A002110, A002275, A031974.

Sequence in context: A195217 A352755 A116677 * A031200 A075479 A081222

Adjacent sequences:  A323057 A323058 A323059 * A323061 A323062 A323063

KEYWORD

nonn,easy

AUTHOR

Patrick A. Thomas, Jan 19 2019

STATUS

approved

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Last modified August 19 16:22 EDT 2022. Contains 356229 sequences. (Running on oeis4.)