How to resolve the algorithm Sequence of non-squares step by step in the ALGOL W programming language
Published on 12 May 2024 09:40 PM
How to resolve the algorithm Sequence of non-squares step by step in the ALGOL W programming language
Table of Contents
Problem Statement
Show that the following remarkable formula gives the sequence of non-square natural numbers:
This is sequence A000037 in the OEIS database.
Let's start with the solution:
Step by Step solution about How to resolve the algorithm Sequence of non-squares step by step in the ALGOL W programming language
Source code in the algol programming language
begin
% check values of the function: f(n) = n + floor(1/2 + sqrt(n)) %
% are not squares %
integer procedure f ( integer value n ) ;
begin
n + entier( 0.5 + sqrt( n ) )
end f ;
logical noSquares;
% first 22 values of f %
for n := 1 until 22 do writeon( i_w := 1, f( n ) );
% check f(n) does not produce a square for n in 1..1 000 000 %
noSquares := true;
for n := 1 until 1000000 do begin
integer fn, rn;
fn := f( n );
rn := round( sqrt( fn ) );
if ( rn * rn ) = fn then begin
write( "Found square at: ", n );
noSquares := false
end if_fn_is_a_square
end for_n ;
if noSquares then write( "f(n) did not produce a square in 1 .. 1 000 000" )
else write( "f(n) produced a square" )
end.
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