A339203 Decimal expansion of the generating constant for the exponents of the Mersenne primes.

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

Offset

1,1

Comments

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

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.

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.

Links

Table of n, a(n) for n=1..88.

Dylan Friedman, Juli Garbulsky, Bruno Glecer, James Grime, and Massi Tron Florentin, A Prime-Representing Constant, 2019.

Formula

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

Example

2.93009444726879573667795218699043578505760116717999...

Crossrefs

Cf. A000043.

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

Sequence in context: A318511 A345299 A276048 * A179451 A124918 A348763

Adjacent sequences: A339200 A339201 A339202 * A339204 A339205 A339206

Keyword

nonn,cons

Author

A.H.M. Smeets, Nov 27 2020

Status

approved