A232240 - OEIS

%I #14 Mar 21 2020 16:22:44

%S 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,

%T 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,

%U 5,4,3,2,1,0,1,2,3,4,5,6,7,8,7,6,7,8,7

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

%C Phi = 1.61803398874989...

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

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

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

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

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

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

%H Harvey P. Dale, <a href="/A232240/b232240.txt">Table of n, a(n) for n = 1..1000</a>

%t 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 *)

%Y Cf. A001622

%K nonn,easy,base

%O 1,2

%A _Philippe Deléham_, Nov 20 2013 at the suggestion of _N. J. A. Sloane_