|
|
A051158
|
|
Decimal expansion of Sum_{n >= 0} 1/(2^2^n+1).
|
|
7
|
|
|
5, 9, 6, 0, 6, 3, 1, 7, 2, 1, 1, 7, 8, 2, 1, 6, 7, 9, 4, 2, 3, 7, 9, 3, 9, 2, 5, 8, 6, 2, 7, 9, 0, 6, 4, 5, 4, 6, 2, 3, 6, 1, 2, 3, 8, 4, 7, 8, 1, 0, 9, 9, 3, 2, 6, 2, 1, 4, 4, 2, 4, 5, 9, 9, 6, 0, 9, 1, 0, 8, 9, 9, 7, 7, 4, 8, 8, 6, 0, 8, 8, 8, 9, 9, 3, 6, 1, 9, 1, 8, 4, 6, 4, 6, 4, 4, 0, 7, 4
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
LINKS
|
S. Audinarayana Moorthy, Problem E2455, The American Mathematical Monthly, Vol. 81, No. 1 (1974), p. 85, solution, ibid., Vol. 82, No. 2 (1975), pp. 173-174.
Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 247.
|
|
FORMULA
|
Equals (1/2) * Sum_{k>=1} A000120(k)/2^k (S. Audinarayana Moorthy, 1974). - Amiram Eldar, May 15 2020
|
|
EXAMPLE
|
0.59606317211782167942...
|
|
MATHEMATICA
|
RealDigits[Sum[1/(2^2^n + 1), {n, 0, 10}], 10, 111][[1]] (* Robert G. Wilson v, Jul 03 2014 *)
|
|
PROG
|
(PARI) /* divisionless routine from fxtbook */
s2(y, N=7)=
{ local(in, y2, A); /* as powerseries correct to order = 2^N-1 */
in = 1; /* 1+y+y^2+y^3+...+y^(2^k-1) */
A = y; for(k=2, N, in *= (1+y); y *= y; A += y*(in + A); );
return( A ); }
a=0.5*s2(0.5) /* computation of the constant 0.596063172117821... */
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
Robert Lozyniak (11(AT)onna.com)
|
|
STATUS
|
approved
|
|
|
|