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A299025 a(n) = the fractional part of 1 / A003592(n) read backwards. 1
0, 5, 52, 2, 521, 1, 5260, 50, 40, 52130, 520, 20, 526510, 5210, 10, 800, 5218700, 52600, 500, 400, 52609300, 521300, 5200, 200, 521359100, 6100, 5265100, 52100, 100, 5265679000, 8000, 52187000, 526000, 5000, 52182884000, 4000, 526093000, 23000, 5213000, 52000 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Numbers in this sequence that also appear in A003592, sorted, include the product of numbers k | 10^e with integer e >= 0 and 10^m with m >= e. For instance, the proper divisors of 10 {1, 2, 5} appear and {10, 20, 40, 50} follow, finally {100, 200, 400, 500, 800} followed by any product k 10^m with k = {1, 2, 4, 5, 8} and m >= 3. - Michael De Vlieger, Feb 03 2018
LINKS
FORMULA
a(A180953(n)) = 10^(n-1) for any n > 0.
EXAMPLE
The first terms, alongside A003592(n) and the fractional part of 1/A003592(n), are:
n a(n) A003592(n) frac(1/A003592(n))
-- ---- ---------- ------------------
1 0 1 0
2 5 2 0.5
3 52 4 0.25
4 2 5 0.2
5 521 8 0.125
6 1 10 0.1
7 5260 16 0.0625
8 50 20 0.05
9 40 25 0.04
10 52130 32 0.03125
11 520 40 0.025
12 20 50 0.02
13 526510 64 0.015625
14 5210 80 0.0125
15 10 100 0.01
16 800 125 0.008
17 5218700 128 0.0078125
18 52600 160 0.00625
19 500 200 0.005
20 400 250 0.004
MATHEMATICA
With[{e = 12}, Table[FromDigits@ Reverse@ PadLeft[#1, Length@ #1 + Abs@ #2] - 10 Boole[n == 1] & @@ RealDigits[1/n], {n, Sort@ Flatten@ Table[2^i*5^j, {i, 0, e}, {j, 0, Log[5, 2^(e - i)]}]}]] (* Michael De Vlieger, Feb 03 2018, after Robert G. Wilson v at A003592 *)
PROG
(PARI) mx = 4000; A003592 = vecsort(concat(vector(1+logint(mx, 2), i, vector(1+logint(floor(mx/2^(i-1)), 5), j, 2^(i-1) * 5^(j-1)))))
backward(n) = my (v=0, i=frac(1/n), r=1/10); while (i, v += r*floor(i); i=frac(i)*10; r*=10); v
print (apply(backward, A003592))
CROSSREFS
Sequence in context: A003515 A022501 A134097 * A247702 A247713 A067282
KEYWORD
nonn,base,easy
AUTHOR
Rémy Sigrist, Feb 01 2018
STATUS
approved

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)