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
Examples
=0.0628722940941970148997691893087506266160327893199480438213105086596888471... = 1/17 + 1/262 + 1/4312 + 1/16779232 + 1/4311709696 + 1/73014280192 + ...
Links
- 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).
Crossrefs
Cf. A000396.
Programs
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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 *)
Extensions
More terms from Jon E. Schoenfield, Aug 19 2015
More terms from Robert G. Wilson v, Dec 15 2015