|
Search: id:A075189
|
|
|
| A075189 |
|
Number of unique primes in the numerator of the 2^n sums generated from the set 1, 1/2, 1/3,..., 1/n. |
|
+0
4
|
|
| 0, 1, 3, 6, 14, 20, 38, 74, 134, 232, 486, 526, 1078, 2036, 2505, 4762, 9929, 14598, 29831, 31521
(list; graph; listen)
|
|
|
OFFSET
|
1,3
|
|
|
COMMENT
|
Every prime is generated eventually. For the largest generated prime, see A075226. For the smallest odd prime not generated, see A075227.
|
|
EXAMPLE
|
a(3) = 3 because 3 sums yield unique prime numerators: 1+1/2 = 3/2, 1/2+1/3 = 5/6 and 1+1/2+1/3 = 11/6.
|
|
MATHEMATICA
|
Needs["DiscreteMath`Combinatorica`"]; maxN=20; For[lst={}; prms={}; i=0; n=1, n<=maxN, n++, While[i<2^n-1, i++; s=NthSubset[i, Range[n]]; k=Numerator[Plus@@(1/s)]; If[PrimeQ[k], prms=Union[prms, {k}]]]; AppendTo[lst, Length[prms]]]; lst
|
|
CROSSREFS
|
Cf. A001008, A075135, A075188, A075226, A075227.
Adjacent sequences: A075186 A075187 A075188 this_sequence A075190 A075191 A075192
Sequence in context: A083356 A096337 A109757 this_sequence A093866 A056596 A026341
|
|
KEYWORD
|
nice,nonn
|
|
AUTHOR
|
T. D. Noe (noe(AT)sspectra.com), Sep 08 2002
|
|
|
Search completed in 0.002 seconds
|
