A354592 Decimal expansion of Sum_{k>=1} (1/k - (1 - log(k)/k)^k).

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

Offset

1,3

Links

Table of n, a(n) for n=1..105.

Example

1.030542353784941208996280929828874607828110554145356713631921644616675...

Maple

Digits := 120: ser := sort(convert(series((1/n - (1 - log(n)/n)^n), n = infinity, 300), polynom), n): s := evalf(sum(op(1, ser), n = 1..infinity), 120): for k from 2 to nops(ser) do serx := expand(op(k, ser)): for j to nops(serx) do s := s + evalf(sum(op(j, serx), n = 1..infinity), 120) end do: print(k, s) end do:

Mathematica

NSum[1/k - (1 - Log[k]/k)^k, {k, 1, Infinity}, WorkingPrecision -> 30, NSumTerms -> 100] (* only 20 digits are correct *)

Crossrefs

Cf. A354450, A354593.

Sequence in context: A144670 A370549 A011078 * A259617 A159060 A021770

Adjacent sequences: A354589 A354590 A354591 * A354593 A354594 A354595

Keyword

nonn,cons

Author

Vaclav Kotesovec, Jun 01 2022

Status

approved