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A078257 a(n) = denominator(N) where N = 0.123...n (concatenation of 1 to n after decimal point). 6
10, 25, 1000, 5000, 20000, 15625, 10000000, 50000000, 1000000000, 10000000000, 10000000000000, 125000000000000, 100000000000000000, 5000000000000000000, 200000000000000000000, 25000000000000000000000, 10000000000000000000000000, 500000000000000000000000000, 100000000000000000000000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Conjecture: sequence is not equal to the sequence of denominators presented in A172495 and A172506. - Jaroslav Krizek, Feb 05 2010
The conjecture is false for both other sequences; see A172495 and A172506 for proofs. - Michael S. Branicky, Nov 30 2022
LINKS
Michael S. Branicky, Table of n, a(n) for n = 1..369
FORMULA
a(n) = denominator(Sum_{k=1..n} k/10^A058183(k)). - Stefano Spezia, Nov 30 2022
EXAMPLE
a(1) = 10 as 10*0.1 = 1, a(2) = 25 as 25*0.12 = 3.
PROG
(PARI) a(n) = {my(s = ""); for (k=1, n, s = concat(s, Str(k))); denominator(eval(s)/10^(#s)); } \\ Michel Marcus, Jan 15 2019
(Python)
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
CROSSREFS
Cf. A058183, A078258 (numerators), A172495, A172506.
Sequence in context: A219377 A156183 A124870 * A059198 A259297 A358774
KEYWORD
base,nonn,frac
AUTHOR
Amarnath Murthy, Nov 24 2002
EXTENSIONS
More terms from Sascha Kurz, Jan 04 2003
More terms from Michel Marcus, Jan 15 2019
STATUS
approved

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Last modified March 5 02:31 EST 2024. Contains 370537 sequences. (Running on oeis4.)