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

1,1

Links

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

Formula

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

Example

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

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 *)

Crossrefs

Cf. A111395.

Sequence in context: A180597 A219242 A330920 * A308414 A360895 A335985

Adjacent sequences: A155813 A155814 A155815 * A155817 A155818 A155819

Keyword

nonn,base

Author

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

Extensions

More terms from Harvey P. Dale, Nov 07 2012

Offset corrected by Robert Israel, Aug 22 2023

Status

approved