A339764 Decimal expansion of Varona's constant = Sum_{k >= 1} prime(k)/2^(k + k!).

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

Offset: 0

Author

José María Grau Ribas, Dec 20 2020

Keywords

• nonn
• cons

Comments

Varona's constant v is transcendental and generates the primes via prime(1)=2=floor(4*v) and for n>1 prime(n) = floor(v*2^(n+n!)) - 2^(1+n!-(n-1)!)*floor(v*2^(n-1+(n-1)!)).

Examples

			0.69726565107703208923339843750000000025860875718090325175312203818889
		

Links

• Juan L. Varona, A couple of transcendental prime-representing constants, arXiv:2012.11750 [math.NT], 2020.
• Index entries for transcendental numbers

Crossrefs

Cf. A249270, A016104, A051021.

Programs

Mathematica

First@RealDigits@N[Sum[Prime[i]/2^(i + i!), {i, 1, 12}], 300]

PARI

suminf(k=1, prime(k)/2^(k + k!)) \\ Michel Marcus, Dec 21 2020