%I #34 Dec 06 2022 09:25:56
%S 11,53,3123,20617,102469,95679,71234567,406172839,9123456789,
%T 101234567891,111234567891011,1515432098637639,1312345678910111213,
%U 70617283945505560657,3024691357820222426283,403086419727527803285379,171234567891011121314151617
%N a(n) = numerator of fraction whose decimal representation is (n).(1)(2)(3)...(n-1)(n).
%C Sequence of denominators: 10, 25, 1000, 5000, 20000, 15625, 10000000, 50000000, 1000000000, 10000000000, ... Conjecture: this sequence is not equal to the sequence A078257.
%C I conjecture that it is the same as A078257. - _Franklin T. Adams-Watters_, Mar 29 2014
%C This sequence of denominators is the same as A078257 up to at least n=10000. - _Jon E. Schoenfield_, Mar 29 2014
%C From _Michael S. Branicky_, Nov 30 2022: (Start)
%C The denominators here are the same as in A078257.
%C 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)
%H Harvey P. Dale, <a href="/A172495/b172495.txt">Table of n, a(n) for n = 1..368</a>
%e a(6) = 95679; 95679/15625 = 6.123456.
%t Numerator[#]GCD[Numerator[#],Denominator[#]]&/@Table[FromDigits[Join[{n},Flatten[ IntegerDigits/@Range[n]]]]/10^n,{n,20}] (* _Harvey P. Dale_, Dec 16 2019 *)
%K nonn,base,frac
%O 1,1
%A _Jaroslav Krizek_, Feb 05 2010
%E a(11)-a(17) from _Jon E. Schoenfield_, Dec 19 2017