A155816 - OEIS

%I #14 Aug 24 2023 07:28:05

%S 7,5,3,2,1,1,8,6,4,3,2,1,1,7,5,3,2,1,1,9,6,4,3,2,1,1,8,6,4,3,2,1,1,7,

%T 5,3,2,1,1,9,6,4,3,2,1,1,8,5,4,2,2,1,1,7,5,3,2,1,1,9,6,4,3,2,1,1,8,5,

%U 4,2,2,1,1,7,5,3,2,1,1,9,6,4,3,2,1,1

%N First nonzero digit in the decimal expansion of (cos Pi/4)^n.

%H Robert Israel, <a href="/A155816/b155816.txt">Table of n, a(n) for n = 1..10000</a>

%F a(2*k) = A111395(k). - _Robert Israel_, Aug 22 2023

%e (cos Pi/4)^4=0.25, so a(4)=2.

%e (cos Pi/4)^8=0.0625, so a(8)=6.

%p f:= proc(n) local t,m;

%p   m:= 1 + ilog10(floor(2^(n/2)));

%p   floor(10^m * 2^(-n/2))

%p end proc:

%p map(f, [$1..100]); # _Robert Israel_, Aug 22 2023

%t With[{c=Cos[Pi/4]},Table[First[RealDigits[N[c^n,20]][[1]]],{n,120}]] (* _Harvey P. Dale_, Nov 07 2012 *)

%Y Cf. A111395.

%K nonn,base

%O 1,1

%A Avik Roy (avik_3.1416(AT)yahoo.co.in), Jan 28 2009

%E More terms from _Harvey P. Dale_, Nov 07 2012

%E Offset corrected by _Robert Israel_, Aug 22 2023