A052110 Decimal expansion of c^c^c^... where c is the constant defined in A037077.

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

Offset: 0

Author

Marvin Ray Burns Jan 20 2000, Mar 28 2008, Nov 08 2009, Mar 24 2010, Jun 27 2011

Keywords

• cons
• nonn

Comments

See (Weisstein) link on Power Tower.

Examples

			0.4619214401644114454085886426141945786350282801364882284434162927358917250...
		

References

• Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 448-452.

Links

• Eric Weisstein's World of Mathematics, Power Tower.
• Gus Wiseman, Tetration.
• OEIS Wiki, Tetration.
• OEIS Wiki, MRB constant.
• Wikipedia, Tetration.

Crossrefs

Cf. A037077, A000027, A000312, A002488, A073230.

Programs

Mathematica

n = 105; M = NSum[(-1)^n*(n^(1/n) - 1), {n, 1, Infinity}, WorkingPrecision -> n + 10, Method -> "AlternatingSigns"]; L = Log[M]; N[-ProductLog[-L]/L, n] (* Marvin Ray Burns, Mar 08 2013 *)

PARI

default(realprecision,66);
M=sumalt(x=1,(-1)^x*((x^(1/x))-1));
solve(x=.46,.462,x^(1/x)-M)

Extensions

Simplified definition by Marvin Ray Burns, Mar 08 2013