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A078257 a(n) = denominator(N) where N = 0.123...n (concatenation of 1 to n after decimal point).

%I A078257 #26 Nov 30 2022 11:38:40
%S A078257 10,25,1000,5000,20000,15625,10000000,50000000,1000000000,10000000000,
%T A078257 10000000000000,125000000000000,100000000000000000,
%U A078257 5000000000000000000,200000000000000000000,25000000000000000000000,10000000000000000000000000,500000000000000000000000000,100000000000000000000000000000
%N A078257 a(n) = denominator(N) where N = 0.123...n (concatenation of 1 to n after decimal point).
%C A078257 Conjecture: sequence is not equal to the sequence of denominators presented in A172495 and A172506. - _Jaroslav Krizek_, Feb 05 2010
%C A078257 The conjecture is false for both other sequences; see A172495 and A172506 for proofs. - _Michael S. Branicky_, Nov 30 2022
%H A078257 Michael S. Branicky, <a href="/A078257/b078257.txt">Table of n, a(n) for n = 1..369</a>
%F A078257 a(n) = denominator(Sum_{k=1..n} k/10^A058183(k)). - _Stefano Spezia_, Nov 30 2022
%e A078257 a(1) = 10 as 10*0.1 = 1, a(2) = 25 as 25*0.12 = 3.
%o A078257 (PARI) a(n) = {my(s = ""); for (k=1, n, s = concat(s, Str(k))); denominator(eval(s)/10^(#s));} \\ _Michel Marcus_, Jan 15 2019
%o A078257 (Python)
%o A078257 from itertools import count, islice
%o A078257 def agen(): # generator of terms
%o A078257     num, den, pow = 0, 1, 0
%o A078257     for n in count(1):
%o A078257         sn = str(n)
%o A078257         num = num*10**len(sn) + n
%o A078257         den *= 10**len(sn)
%o A078257         pow += len(sn)
%o A078257         nr, dr, c2, c5 = num, den, pow, pow
%o A078257         while nr%2 == 0 and c2 > 0: nr //= 2; dr //= 2; c2 -= 1
%o A078257         while nr%5 == 0 and c5 > 0: nr //= 5; dr //= 5; c5 -= 1
%o A078257         yield dr
%o A078257 print(list(islice(agen(), 19))) # _Michael S. Branicky_, Nov 30 2022
%Y A078257 Cf. A058183, A078258 (numerators), A172495, A172506.
%K A078257 base,nonn,frac
%O A078257 1,1
%A A078257 _Amarnath Murthy_, Nov 24 2002
%E A078257 More terms from _Sascha Kurz_, Jan 04 2003
%E A078257 More terms from _Michel Marcus_, Jan 15 2019