|
| |
|
|
A186000
|
|
Consider the list s(1), s(2), ... of numbers that are products of exactly n primes; a(n) is the smallest s(j) whose decimal expansion ends in j.
|
|
1
|
|
|
|
1, 17, 291, 12, 56, 78645, 1350, 192, 896, 7936, 36096, 3072, 14336, 250880, 1247232, 49152, 229376, 4014080, 6718464, 786432, 3670016, 64225280, 45203456000, 12582912, 58720256, 622854144, 219792015360, 201326592, 939524096, 8321499136, 37849399296, 3221225472, 15032385536, 263066746880, 2924872728576, 51539607552, 240518168576, 4209067950080, 7044820107264, 824633720832, 3848290697216
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
COMMENTS
|
For n = 0, 1, 2, ..., the index j corresponding to a(n) is 1, 7, 91, 2, 6, 8645, 50, 2, 6, 36, 96, 2, 6, 80, 232, 2, 6, 80, 64, 2, 6, 80, >6136, 2, 6, 44, > 564, 2, 6, 36, 96, 2, 6, 80, >286, 2, 6, 80, 64, 2, 6, ..., .
|
|
|
LINKS
|
|
|
|
EXAMPLE
|
a(0) = 1 because 1 is the first and only positive integer (A000027) which is not a prime, a semiprime, a triprime, etc.;
a(1) = 17 because 17 is the seventh term of A000040 (it is also the first term of A046883);
a(2) = 291 because 291 is the 91st term of A001358;
a(3) = 12 because 12 is the second term of A014612;
a(4) = 56 because 56 is the sixth term of A014613; etc.
|
|
|
MATHEMATICA
|
nextKthAlmostPrime[n_, k_] := Block[{m = n + 1}, While[ Plus @@ Last /@ FactorInteger@ m != k, m++]; m] (* from Eric Weisstein, Feb 07 2006 *); f[n_] := Block[{c = 1, kp = 2^n}, While[ Mod[kp, 10^Floor[1 + Log10@ c]] != c, c++; kp = nextKthAlmostPrime[kp, n]]; kp]
(* These terms can be crosschecked by: *)
AlmostPrimePi[k_Integer, n_] := Module[{a, i}, a[0] = 1; If[k == 1, PrimePi[n], Sum[PrimePi[n/Times @@ Prime[Array[a, k - 1]]] - a[k - 1] + 1, Evaluate[ Sequence @@ Table[{a[i], a[i - 1], PrimePi[(n/Times @@ Prime[Array[a, i - 1]])^(1/(k - i + 1))]}, {i, k - 1}]]]]] (* Eric W. Weisstein, Feb 07 2006 *)
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn,base
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
|
|
|
STATUS
|
approved
|
| |
|
|
