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A078258 a(n) = numerator(N), where N = 0.123...n (concatenation of 1 to n after decimal point).

%I A078258 #18 Dec 03 2022 17:51:40
%S A078258 1,3,123,617,2469,1929,1234567,6172839,123456789,1234567891,
%T A078258 1234567891011,15432098637639,12345678910111213,617283945505560657,
%U A078258 24691357820222426283,3086419727527803285379,1234567891011121314151617,61728394550556065707580859,12345678910111213141516171819
%N A078258 a(n) = numerator(N), where N = 0.123...n (concatenation of 1 to n after decimal point).
%H A078258 Michael S. Branicky, <a href="/A078258/b078258.txt">Table of n, a(n) for n = 1..369</a>
%F A078258 a(n) = numerator(Sum_{k=1..n} k/10^A058183(k)). - _Stefano Spezia_, Nov 30 2022. (This is simply a restatement of the definition.)
%e A078258 a(4) = 617 = smallest integer multiple of 0.1234, 617 = 5000*(0.1234).
%o A078258 (PARI) a(n) = {my(s = ""); for (k=1, n, s = concat(s, Str(k))); numerator(eval(s)/10^(#s));} \\ _Michel Marcus_, Jan 15 2019
%o A078258 (Python)
%o A078258 from itertools import count, islice
%o A078258 def agen(): # generator of terms
%o A078258     num, den, pow = 0, 1, 0
%o A078258     for n in count(1):
%o A078258         sn = str(n)
%o A078258         num = num*10**len(sn) + n
%o A078258         den *= 10**len(sn)
%o A078258         pow += len(sn)
%o A078258         nr, c2, c5 = num, pow, pow
%o A078258         while nr%2 == 0 and c2 > 0: nr //= 2; c2 -= 1
%o A078258         while nr%5 == 0 and c5 > 0: nr //= 5; c5 -= 1
%o A078258         yield nr
%o A078258 print(list(islice(agen(), 19))) # _Michael S. Branicky_, Nov 30 2022
%Y A078258 Cf. A058183, A078257 (denominators).
%K A078258 base,nonn,frac
%O A078258 1,2
%A A078258 _Amarnath Murthy_, Nov 24 2002
%E A078258 More terms from _Sascha Kurz_, Jan 04 2003
%E A078258 More terms from _Michel Marcus_, Jan 15 2019