A214390 Numerators of Sum_{n>=1} 1/A045542(n).

1, 10, 101, 187, 149, 1021, 33016, 6845, 37447, 343471, 217843, 269387, 652735, 658741, 84404851, 594869, 99801, 19571431, 845870737, 6799977641, 826494610001, 4703352797483, 5311077568679, 5955647363593, 5974287995603, 2396798638405, 2403189712237

Offset: 1

Author

Reinhard Zumkeller, Jul 15 2012

Keywords

• nonn
• frac

Comments

Goldbach-Euler: sum a(n)/A214391(n) -> 1, n -> oo.

Examples

			.      n     a(n) / A214391(n)
. ----------------------------
.      1    3.0
.     10    1.1827024697863866
.    100    1.0142002275801738
.   1000    1.0011756130379812 .
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
• L. Bibiloni, P. Viader, and J. Paradis, On a Series of Goldbach and Euler, Amer. Math. Monthly, 113 (2006), pp. 206-220.

Crossrefs

Cf. A214391 (denominators).

Programs

Haskell

import Data.Ratio ((%), numerator)
a214390 n = a214390_list !! (n-1)
a214390_list = map numerator $ scanl1 (+) $ map (1 %) a045542_list