|
|
A078506
|
|
Decimal expansion of sum of inverses of unrestricted partition function.
|
|
7
|
|
|
2, 5, 1, 0, 5, 9, 7, 4, 8, 3, 8, 8, 6, 2, 9, 3, 9, 5, 3, 2, 3, 6, 8, 3, 4, 7, 2, 7, 4, 1, 5, 4, 6, 5, 4, 5, 1, 6, 8, 3, 5, 3, 1, 9, 4, 4, 9, 5, 5, 1, 4, 7, 6, 8, 1, 9, 0, 8, 0, 6, 2, 9, 9, 6, 5, 0, 8, 3, 8, 4, 5, 3, 2, 9, 0, 4, 4, 6, 1, 8, 4, 2, 3, 8, 1, 9, 2, 5, 8, 7, 1, 4, 6, 2, 8, 2, 7, 8, 0, 9
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Conjecture: this is a transcendental number. - Zhi-Wei Sun, May 24 2023
|
|
LINKS
|
|
|
FORMULA
|
Sum_{n>=1} 1/A000041(n) = 2.510597483886...
|
|
EXAMPLE
|
2.510597483886293953236834727415465451683531944955147681908...
|
|
MATHEMATICA
|
digits = 100; NSum[1/PartitionsP[n], {n, 1, Infinity}, NSumTerms -> 10000, WorkingPrecision -> digits+1] // RealDigits[#, 10, digits]& // First (* Jean-François Alcover, Feb 21 2014 *)
|
|
PROG
|
(PARI)
default(realprecision, 100);
N=10000; x='x+O('x^N);
v=Vec(Ser( 1/eta(x) ) );
s=sum(n=2, #v, 1.0/v[n] )
(PARI) {a(n) = if( n<-1, 0, n++; default( realprecision, n+5); floor( suminf( k=1, 1 / numbpart(k)) * 10^n) % 10)} /* Michael Somos, Feb 05 2011 */
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
EXTENSIONS
|
Corrected digits from position 32 on by Ralf Stephan, Jan 24 2011
|
|
STATUS
|
approved
|
|
|
|