First power of 2 that has leading decimal digits of 12: Difference between revisions

=={{header|Pascal}}==

First convert 2**i -> 10**x => x= ln(2)/ln(10) *i<BR>

The integer part of x is the position of the comma.Only the fraction of x leads to the digits.

Only the first digits are needed.So I think, the accuracy is sufficient, because the results are the same :-)

<lang pascal>program Power2FirstDigits;

uses

sysutils,strUtils;

const

ld10= ln(2)/ln(10);

function FindExp(CntLmt,Number:NativeUint):NativeUint;

var

i,dgts,cnt: NativeUInt;

begin

i := Number;

dgts := 1;

while i >= 10 do

Begin

dgts *= 10;

i := i div 10;

end;

cnt := 0;

i := 0;

repeat

inc(i);

IF trunc(dgts*exp(ln(10)*frac(i*lD10))) = Number then

Begin

inc(cnt);

IF cnt>= CntLmt then

BREAK;

end;

until false;

write('The ',Numb2USA(IntToStr(cnt)),'th occurrence of 2 raised to a power');

write(' whose product starts with "',Numb2USA(IntToStr(number)));

writeln('" is ',Numb2USA(IntToStr(i)));

FindExp := i;

end;

Begin

FindExp(1,12);

FindExp(2,12);

FindExp(45,123);

FindExp(12345,123);

FindExp(678910,123);

end.

cnt := 0;

CntLmt := 678910-10;

for i := 1 to 193060223 do

Begin

x:= 100*exp(ln(10)*frac(i*lD10));

IF trunc(x) = 123 then

Begin

inc(cnt);

IF cnt>= CntLmt then

writeln(cnt:8,i:10,trunc(x):5)

end;

end;

end.</lang>

{{out}}

<pre>

The 1th occurrence of 2 raised to a power whose product starts with "12" is 7

The 2th occurrence of 2 raised to a power whose product starts with "12" is 80

The 45th occurrence of 2 raised to a power whose product starts with "123" is 12,710

The 12,345th occurrence of 2 raised to a power whose product starts with "123" is 3,510,491

The 678,910th occurrence of 2 raised to a power whose product starts with "123" is 193,060,223

//64Bit real 0m43,031s //32Bit real 0m13,363s</pre>