A179547 Transcendental signature sequence of Pi.

1, 2, 3, 4, 1, 5, 2, 6, 3, 7, 4, 1, 8, 5, 2, 9, 6, 3, 10, 7, 4, 1, 1, 11, 8, 5, 2, 2, 12, 9, 6, 3, 3, 13, 10, 7, 4, 1, 4, 14, 1, 11, 8, 5, 2, 5, 15, 2, 12, 9, 6, 3, 6, 16, 3, 13, 10, 7, 4, 1, 7, 17, 4, 14, 1, 11, 8, 5, 2, 8, 18, 5, 15, 2, 12, 9, 6, 3, 9, 19, 6, 16, 3, 13, 10, 7, 4, 1, 10, 20, 7, 17

Offset

1,2

Comments

Let x be a transcendental number greater than 1. S1(x) is the standard signature sequence for an irrational number - sort y = a0 + a1x (for positive integers a0 and a1) and S1 is the sequence of a0 values. S2(x) is the sequence of a0's for sorted y = a0 + a1x + a2x^2, S3(x) is the a0 sequence for y = a0 + a1x + a2x^2 + a3x^3, etc. The transcendental signature sequence is the limit of Sn(x) as n approaches infinity.

Links

L. K. Mitchell, Table of n, a(n) for n=1..10000

Franklin T. Adams-Watters and Eric W. Weisstein, Signature Sequence

Eric Weisstein's World of Mathematics, Transcendental Number

Crossrefs

Cf. A023133 (signature sequence of Pi).

Sequence in context: A087165 A238326 A083480 * A023133 A026280 A115994

Adjacent sequences: A179544 A179545 A179546 * A179548 A179549 A179550

Keyword

easy,nonn

Author

Kerry Mitchell, Jul 19 2010

Status

approved