A382178
a(n) is the least k > 1 such that the factorial base expansion of k*n starts with that of n.
Original entry on oeis.org
2, 2, 3, 3, 3, 3, 4, 18, 18, 17, 17, 16, 4, 19, 19, 18, 18, 101, 4, 115, 114, 110, 110, 18, 5, 203, 199, 192, 189, 183, 28, 187, 27, 179, 177, 1341, 180, 176, 26, 170, 168, 165, 1320, 168, 1277, 1251, 162, 159, 5, 1649, 204, 1598, 1579, 1551, 200, 197, 195
Offset: 0
The first terms, in decimal and in factorial base, are:
n a(n) fact(n) fact(a(n)*n)
-- ---- ------- ------------
0 2 0 0
1 2 1 1,0
2 3 1,0 1,0,0
3 3 1,1 1,1,1
4 3 2,0 2,0,0
5 3 2,1 2,1,1
6 4 1,0,0 1,0,0,0
7 18 1,0,1 1,0,1,0,0
8 18 1,1,0 1,1,0,0,0
9 17 1,1,1 1,1,1,1,1
10 17 1,2,0 1,2,0,1,0
11 16 1,2,1 1,2,1,1,0
12 4 2,0,0 2,0,0,0
13 19 2,0,1 2,0,1,0,1
14 19 2,1,0 2,1,0,1,0
15 18 2,1,1 2,1,1,0,0
-
A153880(n) = { my (v = 0, f = 1); for (r = 2, oo, if (n==0, return (v);); v += (n%r) * f *= r; n \= r;); }
a(n) = { if (n==0, return (2)); my (m = n, f = 1, e); for (r = 2, oo, m = A153880(m); f *= r; e = (-m) % n; if (e < f, return ((m+e)/n););); }
A382184
a(n) is the least k >= 0 such that the factorial base expansion of n starts with that of k while the remaining digits are zeros.
Original entry on oeis.org
0, 1, 1, 3, 4, 5, 1, 7, 3, 9, 10, 11, 4, 13, 5, 15, 16, 17, 18, 19, 20, 21, 22, 23, 1, 25, 7, 27, 28, 29, 3, 31, 9, 33, 34, 35, 10, 37, 11, 39, 40, 41, 42, 43, 44, 45, 46, 47, 4, 49, 13, 51, 52, 53, 5, 55, 15, 57, 58, 59, 16, 61, 17, 63, 64, 65, 66, 67, 68, 69
Offset: 0
The first terms, in decimal and in factorial base, are:
n a(n) fact(n) fact(a(n))
-- ---- ------- ----------
0 0 0 0
1 1 1 1
2 1 1,0 1
3 3 1,1 1,1
4 4 2,0 2,0
5 5 2,1 2,1
6 1 1,0,0 1
7 7 1,0,1 1,0,1
8 3 1,1,0 1,1
9 9 1,1,1 1,1,1
10 10 1,2,0 1,2,0
11 11 1,2,1 1,2,1
12 4 2,0,0 2,0
13 13 2,0,1 2,0,1
14 5 2,1,0 2,1
15 15 2,1,1 2,1,1
-
a(n) = { if (n, my (m = n, s = oo, d); for (r = 2, oo, if (m==0 || s==0, break, d = m%r, s = min(s, r-1-d);); m \= r;); if (s, my (v = 0); for (r = 2, oo, if (n==0, return (v), v += (n%r) * max(0, r-1-s)!; n \= r;);););); return (n); }
Showing 1-2 of 2 results.
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