A245257 Decimal expansion of y_3, the third of four non-explicit constants recursively derived from Khintchine's [Khinchin's] constant.

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

Offset

1,1

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 1.8.1 Alternative representations [of real numbers], p. 63.

Links

Table of n, a(n) for n=1..105.

Herman P. Robinson, Mathematical Constants.

Example

2.224751480980583015375598924924190424236366707982466701694563315747...

Mathematica

K = Khinchin; a[0] = pi[0] = 2; pi[n_] := Product[a[i], {i, 0, n}]; Clear[a]; a[n_?EvenQ] := a[n] = Floor[K^(n+1)/pi[n-1]]; a[n_?OddQ] := a[n] = Ceiling[K^(n+1)/pi[n-1]]; FromContinuedFraction[Array[a, 300, 0]] // RealDigits[#, 10, 105]& // First

Crossrefs

Cf. A002210, A245255, A245256, A245258.

Sequence in context: A182027 A005865 A176051 * A153988 A253059 A098705

Adjacent sequences: A245254 A245255 A245256 * A245258 A245259 A245260

Keyword

nonn,cons

Author

Jean-François Alcover, Jul 15 2014

Status

approved