A078257
a(n) = denominator(N) where N = 0.123...n (concatenation of 1 to n after decimal point).
Original entry on oeis.org
10, 25, 1000, 5000, 20000, 15625, 10000000, 50000000, 1000000000, 10000000000, 10000000000000, 125000000000000, 100000000000000000, 5000000000000000000, 200000000000000000000, 25000000000000000000000, 10000000000000000000000000, 500000000000000000000000000, 100000000000000000000000000000
Offset: 1
a(1) = 10 as 10*0.1 = 1, a(2) = 25 as 25*0.12 = 3.
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a(n) = {my(s = ""); for (k=1, n, s = concat(s, Str(k))); denominator(eval(s)/10^(#s));} \\ Michel Marcus, Jan 15 2019
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from itertools import count, islice
def agen(): # generator of terms
num, den, pow = 0, 1, 0
for n in count(1):
sn = str(n)
num = num*10**len(sn) + n
den *= 10**len(sn)
pow += len(sn)
nr, dr, c2, c5 = num, den, pow, pow
while nr%2 == 0 and c2 > 0: nr //= 2; dr //= 2; c2 -= 1
while nr%5 == 0 and c5 > 0: nr //= 5; dr //= 5; c5 -= 1
yield dr
print(list(islice(agen(), 19))) # Michael S. Branicky, Nov 30 2022
A078261
a(n) = numerator(N) where N = 0.246...(2n) is the concatenation of the first n even numbers after the decimal point.
Original entry on oeis.org
1, 6, 123, 617, 24681, 6170253, 1234050607, 30851265177, 12340506070809, 123405060708091, 123405060708091011, 1542563258851137639, 1234050607080910111213, 61702530354045505560657, 2468101214161820222426283, 308512651770227527803285379, 123405060708091011121314151617
Offset: 1
Cf.
A078258 (similar, with concatenation of 1 to n),
A078260 (denominators).
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a:= n-> (t-> numer(t/10^length(t)))(parse(cat(2*i$i=1..n))):
seq(a(n), n=1..17); # Alois P. Heinz, Jun 25 2025
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a(n) = {my(s = ""); for (k=1, n, s = concat(s, Str(2*k))); numerator(eval(s)/10^(#s));} \\ Michel Marcus, Jan 15 2019
More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 19 2003
A172506
a(n) = numerator of fraction a/b, where gcd(a, b) = 1, whose decimal representation has the form (1)(2)(3)...(n-1)(n).(1)(2)(3)...(n-1)(n).
Original entry on oeis.org
11, 303, 123123, 6170617, 246902469, 1929001929, 12345671234567, 617283906172839, 123456789123456789, 123456789101234567891, 12345678910111234567891011, 15432098637639015432098637639, 1234567891011121312345678910111213, 6172839455055606570617283945505560657
Offset: 1
a(6) = 1929001929; 1929001929/15625 = 123456.123456.
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from itertools import count, islice
def agen(): # generator of terms
k, den, pow = 0, 1, 0
for n in count(1):
sn = str(n)
k = k*10**len(sn) + n
den *= 10**len(sn)
pow += len(sn)
nr, c2, c5 = k*(den+1), pow, pow
while nr%2 == 0 and c2 > 0: nr //= 2; c2 -= 1
while nr%5 == 0 and c5 > 0: nr //= 5; c5 -= 1
yield nr
print(list(islice(agen(), 19))) # Michael S. Branicky, Nov 30 2022
Showing 1-3 of 3 results.
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