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a(n) = numerator(N), where N = 0.123...n (concatenation of 1 to n after decimal point).
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%I #18 Dec 03 2022 17:51:40

%S 1,3,123,617,2469,1929,1234567,6172839,123456789,1234567891,

%T 1234567891011,15432098637639,12345678910111213,617283945505560657,

%U 24691357820222426283,3086419727527803285379,1234567891011121314151617,61728394550556065707580859,12345678910111213141516171819

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

%H Michael S. Branicky, <a href="/A078258/b078258.txt">Table of n, a(n) for n = 1..369</a>

%F 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 a(4) = 617 = smallest integer multiple of 0.1234, 617 = 5000*(0.1234).

%o (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 (Python)

%o from itertools import count, islice

%o def agen(): # generator of terms

%o num, den, pow = 0, 1, 0

%o for n in count(1):

%o sn = str(n)

%o num = num*10**len(sn) + n

%o den *= 10**len(sn)

%o pow += len(sn)

%o nr, c2, c5 = num, pow, pow

%o while nr%2 == 0 and c2 > 0: nr //= 2; c2 -= 1

%o while nr%5 == 0 and c5 > 0: nr //= 5; c5 -= 1

%o yield nr

%o print(list(islice(agen(), 19))) # _Michael S. Branicky_, Nov 30 2022

%Y Cf. A058183, A078257 (denominators).

%K base,nonn,frac

%O 1,2

%A _Amarnath Murthy_, Nov 24 2002

%E More terms from _Sascha Kurz_, Jan 04 2003

%E More terms from _Michel Marcus_, Jan 15 2019