A232240 A walk based on the digits of the golden ratio phi = (1+sqrt(5))/2 (A001622).

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

Offset

1,2

Comments

Phi = 1.61803398874989...

Between 1 and 6 we place 2, 3, 4 and 5.

Between 6 and 1 we place 5, 4, 3 and 2.

Between 1 and 8 we place 2, 3, 4, 5, 6 and 7.

Between 8 and 0 we place 7, 6, 5, 4, 3, 2 and 1, and so on.

This gives 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 7, 6, ...

This could be called a walk (or promenade) on the digits of phi.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Mathematica

dgphi[{a_, b_}]:=Which[a<b, Range[a, b-1], a>b, Range[a, b+1, -1], True, {a}]; dgphi/@ Partition[RealDigits[GoldenRatio, 10, 30][[1]], 2, 1]// Flatten (* Harvey P. Dale, Mar 21 2020 *)

Crossrefs

Cf. A001622

Sequence in context: A271832 A063260 A271859 * A073793 A017891 A017881

Adjacent sequences: A232237 A232238 A232239 * A232241 A232242 A232243

Keyword

nonn,easy,base

Author

Philippe Deléham, Nov 20 2013 at the suggestion of N. J. A. Sloane

Status

approved