A095713 - OEIS

%I #6 Jan 14 2025 20:50:50

%S 1,6,1,1,6,1,8,1,6,1,0,8,1,6,1,3,0,8,1,6,1,3,3,0,8,1,6,1,9,3,3,0,8,1,

%T 6,1,8,9,3,3,0,8,1,6,1,8,8,9,3,3,0,8,1,6,1,7,8,8,9,3,3,0,8,1,6,1,4,7,

%U 8,8,9,3,3,0,8,1,6,1,9,4,7,8,8,9,3,3,0,8,1,6,1,8,9,4,7,8,8,9,3,3,0,8,1,6,1

%N Triangle of numbers obtained by reversing the first n digits of golden ratio phi and juxtaposing.

%e Triangle begins:

%e   1;

%e   6,1;

%e   1,6,1;

%e   8,1,6,1;

%e   0,8,1,6,1;

%e   ... (reverse order of 1; 1.6; 1.61; 1.618; 1.6180;...)

%t nn=20;With[{gr=RealDigits[GoldenRatio,10,nn][[1]]},Flatten[Table[ Reverse[ Take[gr,n]],{n,nn}]]] (* _Harvey P. Dale_, Jul 16 2012 *)

%o (PARI) a(n)=if(n<1,0,default(realprecision,n+2);floor((1/2+sqrt(5)/2)*10^(n-1))%10);

%o b(n)=1+binomial(1+floor(1/2+sqrt(2*n)),2)-n;

%o for(n=1,120,print1(a(b(n))", "))

%Y Cf. A001622.

%K base,easy,nonn,tabl

%O 1,2

%A Herman Jamke (hermanjamke(AT)fastmail.fm), Jul 07 2004