A155816 First nonzero digit in the decimal expansion of (cos Pi/4)^n.

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

Offset: 1

Author

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

Keywords

• nonn
• base

Examples

			(cos Pi/4)^4=0.25, so a(4)=2.
(cos Pi/4)^8=0.0625, so a(8)=6.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A111395.

Programs

Maple

f:= proc(n) local t,m;
  m:= 1 + ilog10(floor(2^(n/2)));
  floor(10^m * 2^(-n/2))
end proc:
map(f, [$1..100]); # Robert Israel, Aug 22 2023

Mathematica

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

Formula

a(2*k) = A111395(k). - Robert Israel, Aug 22 2023

Extensions

More terms from Harvey P. Dale, Nov 07 2012

Offset corrected by Robert Israel, Aug 22 2023