A016104 -id:A016104 - cp's OEIS frontend

A086238 Decimal expansion of Omega prime-generating constant.

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

Offset: 1

Eric W. Weisstein, Jul 12 2003

This constant generates A016104, an infinite sequence of primes with a tetrational rate of growth. - Charles R Greathouse IV, Jul 26 2013

			1.9287821871502166838954018709323669423037706093899360023878280792029...

Stephen Finch, Mathematical Constants, Cambridge University Press, 2003, p. 131.
Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See pp. 137-138.

Eric Weisstein's World of Mathematics, Prime Formulas

More terms from Charles R Greathouse IV, Jul 26 2013

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

Original entry on oeis.org

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

José María Grau Ribas, Dec 20 2020

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)!)).

			0.69726565107703208923339843750000000025860875718090325175312203818889

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

Cf. A249270, A016104, A051021.

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

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

cp's OEIS Frontend

A086238 Decimal expansion of Omega prime-generating constant.

Views

Author

Keywords

Comments

Examples

References

Links

Extensions

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI