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

Author

A.H.M. Smeets, Nov 27 2020

Keywords

• nonn
• cons

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.

Examples

			2.93009444726879573667795218699043578505760116717999...
		

Links

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

Crossrefs

Cf. A000043.

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

Formula

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