It is then a composite of the first sums, and hardly a constant, as I had hoped.
Reconstructing early and very early methods is a part of my profession, playing with numbers a hobby of mine. Here is a quick approximation of Euler's gamma found yesterday:
1 minus ln(1) minus '7 of 3 1 '2 minus ln(2) minus '13 of 3 1 '2 '3 minus ln(3) minus '19 of 3 1 '2 '3 '4 minus ln(4) minus '25 of 3
Gauss connected the natural logarithm with pi, while Euler combined pi and the primes in the infinite product 3/2 x 5/6 x 7/4 x 11/10 x 13/14 x 17/18 x 19/18 x 23/22... approximating pi/2, containing the odd primes and the neighboring numbers that don't contain 4 as factor.
I shall go on playing with number patterns, fascinated by how quickly the natural numbers lead to the natural logarithm, and the odd numbers to pi.