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

1, 3, 123, 617, 2469, 1929, 1234567, 6172839, 123456789, 1234567891, 1234567891011, 15432098637639, 12345678910111213, 617283945505560657, 24691357820222426283, 3086419727527803285379, 1234567891011121314151617, 61728394550556065707580859, 12345678910111213141516171819

Offset

1,2

Links

Michael S. Branicky, Table of n, a(n) for n = 1..369

Formula

a(n) = numerator(Sum_{k=1..n} k/10^A058183(k)). - Stefano Spezia, Nov 30 2022. (This is simply a restatement of the definition.)

Example

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

Prog

(PARI) a(n) = {my(s = ""); for (k=1, n, s = concat(s, Str(k))); numerator(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, c2, c5 = num, 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

Crossrefs

Cf. A058183, A078257 (denominators).

Sequence in context: A171357 A209363 A012569 * A258658 A222186 A124246

Adjacent sequences: A078255 A078256 A078257 * A078259 A078260 A078261

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