A133362 Decimal expansion of 1/(2 log 2).

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

Offset: 0

Author

Jonathan Vos Post, Oct 26 2007

Keywords

• cons
• easy
• nonn

Comments

PrimePi(n) = A000720(n) => (log n)/(2 log 2) for all n > 2. An elegant proof is given in Kontoyiannis.

Base 4 logarithm of the natural logarithm base. - Alonso del Arte, Aug 31 2014

Examples

			0.7213475204444817036799623405009460...
		

References

• Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.7 Lengyel's constant p. 319 and Section 5.11 Feller's coin tossing p. 341.

Links

• Ioannis Kontoyiannis, Some information-theoretic computations related to the distribution of prime numbers, arXiv:0710.4076 [cs.IT], 2007.
• Index entries for transcendental numbers

Crossrefs

Cf. A000720, A016627 (reciprocal).

Programs

Maple

Digits:=100: evalf(0.5/log(2)); # R. J. Mathar, Nov 09 2007

Mathematica

RealDigits[1/(2Log[2]), 10, 128][[1]] (* Alonso del Arte, Aug 31 2014 *)

PARI

1/log(4) \\ Charles R Greathouse IV, Mar 24 2016

Extensions

More terms from R. J. Mathar, Nov 09 2007