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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
One could just as well sum from n >= 0, giving a value one higher. - Franklin T. Adams-Watters, Nov 30 2018
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
Sequence in context: A329251 A062627 A011217 * A323909 A124779 A284750
KEYWORD
cons,nonn
AUTHOR
Ralf Stephan, Jan 05 2003
EXTENSIONS
Corrected digits from position 32 on by Ralf Stephan, Jan 24 2011
More terms from Jean-François Alcover, Feb 21 2014
STATUS
approved

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Last modified April 13 09:16 EDT 2024. Contains 371640 sequences. (Running on oeis4.)