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

Author

Kerry Mitchell, Jul 19 2010

Keywords

• easy
• nonn

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).