A259931 Decimal expansion of the sum of the reciprocals of the averages of adjacent pairs of perfect numbers (A000396).

0, 6, 2, 8, 7, 2, 2, 9, 4, 0, 9, 4, 1, 9, 7, 0, 1, 4, 8, 9, 9, 7, 6, 9, 1, 8, 9, 3, 0, 8, 7, 5, 0, 6, 2, 6, 6, 1, 6, 0, 3, 2, 7, 8, 9, 3, 1, 9, 9, 4, 8, 0, 4, 3, 8, 2, 1, 3, 1, 0, 5, 0, 8, 6, 5, 9, 6, 8, 8, 8, 4, 7, 1, 2, 3, 5, 8, 5, 7, 2, 1, 4, 9, 7, 5, 5, 2, 9, 5, 0, 0, 7, 7, 1, 0, 4, 3, 0, 7, 7, 8, 4, 1, 2, 0, 0

Offset

0,2

Links

Table of n, a(n) for n=0..105.

Jonathan Bayless and Dominic Klyve, Reciprocal sums as a knowledge metric, Amer Math Monthly 120 (November, 2013) 822-831.

Steven Finch, Amicable Pairs and Aliquot Sequences, Oct 31 2013. [Cached copy, with permission of the author]

MathOverflow, Sum of the reciprocal of perfect numbers, Jun 10 2012.

José Camacho Medina's Matematico Fresnillense, La Constante entre Numeros Perfectos (in Spanish).

Formula

Equals Sum_{n>=1} 2/(A000396(n) + A000396(n+1)).

Equals Sum_{n>=1} 1/A259849(n).

Example

=0.0628722940941970148997691893087506266160327893199480438213105086596888471...
= 1/17 + 1/262 + 1/4312 + 1/16779232 + 1/4311709696 + 1/73014280192 + ...

Mathematica

exp = {2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521} (* see A000043 *); pn[k_] := 2^(exp[[k]] - 1)(2^exp[[k]] - 1); RealDigits[Sum[2/(pn[k] + pn[k + 1]), {k, 1, 12}], 10, 111][[1]] (* Robert G. Wilson v, Dec 15 2015 *)

Crossrefs

Cf. A000396.

Sequence in context: A155687 A021618 A085589 * A333350 A332092 A021163

Adjacent sequences: A259928 A259929 A259930 * A259932 A259933 A259934

Keyword

nonn,cons

Author

José de Jesús Camacho Medina, Aug 17 2015

Extensions

More terms from Jon E. Schoenfield, Aug 19 2015

More terms from Robert G. Wilson v, Dec 15 2015

Status

approved