login
A155816
First nonzero digit in the decimal expansion of (cos Pi/4)^n.
1
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
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
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