OFFSET
1,1
COMMENTS
Sequence of denominators: 10, 25, 1000, 5000, 20000, 15625, 10000000, 50000000, 1000000000, 10000000000, ... Conjecture: this sequence is not equal to the sequence A078257.
I conjecture that it is the same as A078257. - Franklin T. Adams-Watters, Mar 29 2014
This sequence of denominators is the same as A078257 up to at least n=10000. - Jon E. Schoenfield, Mar 29 2014
From Michael S. Branicky, Nov 30 2022: (Start)
The denominators here are the same as in A078257.
Proof. Let Cn denote the concatenation (1)(2)(3)...(n-1)(n) and En its number of decimal digits. The unreduced numerators and denominators of A078257(n) are Cn and 10^En; for a(n), they are (n*10^En + Cn) and 10^En. To find A078257(n), we continue to divide the unreduced numerator by 2 and 5 as long as that is possible. For a(n) to be smaller, we would have to "get past" all the decimal digits in Cn and divide n at least once. But if we could do that, it would be a contradiction to earlier terms of A078257. (End)
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..368
EXAMPLE
a(6) = 95679; 95679/15625 = 6.123456.
MATHEMATICA
Numerator[#]GCD[Numerator[#], Denominator[#]]&/@Table[FromDigits[Join[{n}, Flatten[ IntegerDigits/@Range[n]]]]/10^n, {n, 20}] (* Harvey P. Dale, Dec 16 2019 *)
CROSSREFS
KEYWORD
nonn,base,frac
AUTHOR
Jaroslav Krizek, Feb 05 2010
EXTENSIONS
a(11)-a(17) from Jon E. Schoenfield, Dec 19 2017
STATUS
approved