A339203 - OEIS

%I #31 Nov 28 2020 20:21:16

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

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

%U 4,4,4,1,7,8,3,5,9,9,4,1,0,7,8,3,2,5,8,7

%N Decimal expansion of the generating constant for the exponents of the Mersenne primes.

%C Inspired by the prime generating constant A249270, but here for the exponents of the Mersenne primes, A000043(n).

%C The producing function is given by f' = floor(f)*(f-floor(f)+1), starting with this constant, f' denoting the next f, and floor(f) being the next term of the sequence being produced by this constant.

%C Note that this constant is useless in trying to predict the next Mersenne prime exponent. A new known next Mersenne prime exponent will only enable us to calculate this constant more precisely.

%H Dylan Friedman, Juli Garbulsky, Bruno Glecer, James Grime, and Massi Tron Florentin, <a href="https://www.researchgate.net/publication/330746181_A_Prime-Representing_Constant">A Prime-Representing Constant</a>, 2019.

%F Equals Sum_{n > 0} (A000043(n)-1)/(Product_{k = 1..n-1} A000043(k)).

%e 2.93009444726879573667795218699043578505760116717999...

%Y Cf. A000043.

%Y Cf. A249270 (for primes), A339204 (for Fibonacci numbers).

%K nonn,cons

%O 1,1

%A _A.H.M. Smeets_, Nov 27 2020