|
|
A121240
|
|
Numerator of sum_{k=1..n} 1/2^prime(k).
|
|
2
|
|
|
1, 3, 13, 53, 849, 3397, 54353, 217413, 3478609, 222630977, 890523909, 56993530177, 911896482833, 3647585931333, 58361374901329, 3735127993685057, 239048191595843649, 956192766383374597, 61196337048535974209
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
a(n) is prime for n = {2, 3, 4, 10, 21, 321,..} where it takes the values {3, 13, 53, 222630977, ...}.
The prime constant A051006 = 0.414682509.. is limit(n->infinity) a(n)/2^prime(n) .
|
|
LINKS
|
|
|
FORMULA
|
a(n) = Numerator[ Sum[ 1/2^Prime[k], {k,1,n} ] ]. a(n) = A072762[ Prime[n] ].
|
|
MATHEMATICA
|
Table[Numerator[Sum[1/2^Prime[k], {k, 1, n}]], {n, 1, 30}]
Accumulate[1/2^Prime[Range[30]]]//Numerator (* Harvey P. Dale, Aug 11 2021 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
frac,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|