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A135096 Decimal expansion of certain constant L. 1

%I #6 Oct 15 2014 13:36:42

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

%T 6,1,9,1,2,1,5,9,6,2,1,7,1,5,6

%N Decimal expansion of certain constant L.

%C Conjecture: With any real number c in the interval [L,U] there exists for each natural number n>2 a natural number m and a prime number p so that n=floor(m^c)+p. L is the lower bound of c. U is the upper bound of c. L = 0.5781296526305628137240577579803... U = 1.3652123889685187297293386676777... (A135097).

%C L is close to the Euler-Mascheroni constant Gamma = 0.5772... I am continuing calculating further digits.

%e Let c=1.23456789 (arbitrary). Each natural number n>2 has the form n=floor(m^1.23456789+p), where m is natural number and p prime.

%Y Cf. A135097.

%K cons,nonn

%O 0,1

%A _Werner D. Sand_, Nov 25 2007, Dec 01 2007

%E Leading zero removed by _R. J. Mathar_, Feb 05 2009

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