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A211706
Binary expansion of Sum_{n>=1} A006218(n)*2^(-n).
4
1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0
OFFSET
2
COMMENTS
With offset 1 this is the binary expansion of the Erdős-Borwein constant (A065442). Erdős (1948) proved that this constant is irrational by showing that its binary expansion has arbitrarily long strings of zeros. - Amiram Eldar, Aug 01 2020
LINKS
David H. Bailey and Richard E. Crandall, Random generators and normal numbers, Experimental Mathematics, Vol. 11, No. 4 (2002), pp. 527-546. See p. 540.
Paul Erdős, On Arithmetical Properties of Lambert Series, J. Indian Math. Soc., Vol. 12 (1948), 63-66.
EXAMPLE
11.00110110101000001011111100111100100001...
MATHEMATICA
f[n_, m_] := Sum[Floor[n/k], {k, 1, m}]
t = Table[f[n, 100], {n, 1, 4000}] ;
N[Sum[t[[n]]/2^n, {n, 1, 4000}], 100]
RealDigits[%, 10] (* A211705 *)
RealDigits[%%, 2] (* A211706 *)
CROSSREFS
Cf. A006218, A065442, A211701, A211705 (decimal representation)
Sequence in context: A265698 A267673 A267845 * A267683 A267869 A068434
KEYWORD
nonn,cons,base
AUTHOR
Clark Kimberling, Apr 19 2012
EXTENSIONS
Offset changed from Bruno Berselli, May 14 2012
STATUS
approved