A179548 Transcendental signature sequence of e.

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

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

Kerry 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

Sequence in context: A023117 A023127 A125159 * A023119 A118276 A023123

Adjacent sequences: A179545 A179546 A179547 * A179549 A179550 A179551

Keyword

easy,nonn,changed

Author

Kerry Mitchell, Jul 19 2010

Status

approved