A159200 - OEIS

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A159200

Decimal expansion of Sum(k=1;inf)(1/(10^(4*k+2)-1))-(1/(10^(2*k+1)-1)).

0, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 3, 0, 1, 0, 1, 0, 3, 0, 1, 0, 2, 0, 3, 0, 1, 0, 1, 0, 3, 0, 3, 0, 1, 0, 3, 0, 1, 0, 1, 0, 5, 0, 1, 0, 2, 0, 3, 0, 1, 0, 3, 0, 3, 0, 1, 0, 1, 0, 5, 0, 3, 0, 1, 0, 3, 0, 1, 0, 1, 0, 5, 0, 3, 0, 1, 0, 4, 0, 1, 0, 3, 0, 3, 0, 1, 0, 3, 0, 3, 0, 3, 0, 1, 0, 5, 0 (list; constant; graph; refs; listen; history; text; internal format)

	OFFSET	`0,9`
	COMMENTS	`= Sum(k=1;inf) 1/((2^(4k+2)5^(4k+2))-1) - 1/((2^(2k+1)5^(2k+1))-1).` `And Sum(k=1;inf) (1/(10^(k)-1)) / ((1/(10^(4k+2)-1))-(1/(10^(2k+1)-1)))` `= Sum(k=1;inf)A073668 / ((1/(10^(4k+2)-1))-(1/(10^(2k+1)-1))) = -1.111...` `My idea for this decimal expansion come from` `the Engel Expansion of(e) A000027 and the Engel Expansion of(e^-1) A059193` `where a(n)=2(2n+1)(n-1), and i have transformed it into (2n+1)^2-(6n+3).` `It appears that Engel Expansion of 1/e works like a Sundaram sieve.`
	LINKS	`Table of n, a(n) for n=0..99.` `Crible de Sundaram`
	EXAMPLE	`-0.00101010201010301010301020301010303010301010501020301030301...`
	CROSSREFS	`Sequence in context: A067432 A192174 A129308 * A219201 A033764 A033784` `Adjacent sequences: A159197 A159198 A159199 * A159201 A159202 A159203`
	KEYWORD	`cons,nonn`
	AUTHOR	`Eric Desbiaux, Apr 06 2009`
	STATUS	`approved`

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Last modified June 19 04:22 EDT 2013. Contains 226390 sequences.