A172495 a(n) = numerator of fraction whose decimal representation is (n).(1)(2)(3)...(n-1)(n).

11, 53, 3123, 20617, 102469, 95679, 71234567, 406172839, 9123456789, 101234567891, 111234567891011, 1515432098637639, 1312345678910111213, 70617283945505560657, 3024691357820222426283, 403086419727527803285379, 171234567891011121314151617

Offset: 1

Author

Jaroslav Krizek, Feb 05 2010

Keywords

• nonn
• base
• frac

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)

Examples

			a(6) = 95679; 95679/15625 = 6.123456.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..368

Programs

Mathematica

Numerator[#]GCD[Numerator[#],Denominator[#]]&/@Table[FromDigits[Join[{n},Flatten[ IntegerDigits/@Range[n]]]]/10^n,{n,20}] (* Harvey P. Dale, Dec 16 2019 *)

Extensions

a(11)-a(17) from Jon E. Schoenfield, Dec 19 2017