Here is a series of a few source codes on Series and Numbers. The series are nothing only logic and the relations between the numbers all you have to find.
Fibonacci Series, a series of numbers in which each member is the sum of the two preceding numbers. Discovered by Italian mathematician Leonardo Fibonacci. Example - 1,1,2,3,5,8,...etc
//C - Fibonacci Series
#include <stdio.h>
#include <conio.h>
void fibo(int n)
{
int i,a=1,b=0,c;
for(i=1;i<=n;i++)
{
printf("%d ",c);
c=a+b;
a=b;
b=c;
}
}
void main()
{
int n;
clrscr();
printf("\nEnter The Term : ");
scanf("%d",&n);
fibo(n);
getch();
}
Non- Fibonacci Series – The numbers between the
//C – Non-Fibonacci Series
#include <stdio.h>
#include <conio.h>
void Nfibo(int n)
{
int i,a=1,b=0,c,j;
for(i=1;i<=n;i++)
{
c=a+b;
for(j=b+11;i<c;j++)
{
printf("%d ",j);
}
a=b;
b=c;
}
}
void main()
{
int n;
clrscr();
printf("\nEnter The Term : ");
scanf("%d",&n);
Nfibo(n);
getch();
}
Series : 0 7 26 63 124 ...n : It is a simple logical series, just deduct 1 from the cube of each values of natural nos. from 1 to ‘n’.
#include <stdio.h>
#include <conio.h>
void main()
{
int i,n;
printf("\nEnter the Terms : ");
scanf("%d",&n);
clrscr();
for(i=1;i<=n;i++)
{
printf("%d ",(i*i*i)-1);
}
printf("\n\npress any key to Cont...");
getch();
}
Sum of the series 1/2 + 1/3 + 1/4 + … 1/n
#include <stdio.h>
#include <conio.h>
void main()
{
int i,n;
float sum =0;
clrscr();
printf("\nEnter the Terms : ");
scanf("%d",&n);
for(i=1;i<=n;i++)
{
sum=sum+1.0/i;
}
printf("Sum of the Series = %10.3f ",sum);
printf("\n\nPress any key to Cont...");
getch();
}
Taylor Series Formula or Sine Series – To find the sine of a given angle.
x – x3/3! + x5/5! – x7/7! + x9/9! – x11/11!
#include <stdio.h>
#include <conio.h>
oid sinx(float,float);
float pw(float, int);
void main()
{
int ang;
float sum,x;
clrscr();
printf("Enter the angle");
scanf("%d",&ang);
x=ang/180.0*3.1415;
sum=x;
sinx(sum,x);
}
void sinx(float sum, float x)
{
int i,t,j;
float f=1;
for(i=3;i<=9;i=i+2)
{
f=f*i*(i-1)*-1;
sum=sum+pw(x,i)/f;
}
printf("\nSine of %d angle is %f by Taylor Series ",ang,sum);
}
float pw(float x,int i)
{
int j;
float y=1;
for(j=1;j<=i;j++)
{
y=y*x;
}
return y;
}
Even Series – To find Cosine of a given angle.
1 – x2/2! + x4/4! – x6/6! + x8/8! – x10/10!
#include <stdio.h>
#include <conio.h>
#include <math.h>
void main()
{
int ang,i;
float rad,fact=1,sum;
clrscr();
printf("\nEnter an angle ");
scanf("%d",&ang);
rad=22/7.0*ang/180.0;
sum=1;
for(i=2;i<=12;i=i+2)
{
fact=fact*(i)*(i-1)*(-1);
sum=sum+pow(rad,i)/fact;
}
printf("Cosine of %d angle is %10.6f %f ",ang,sum,cos(rad));
getch();
}
Smith No. – is a number whose sum of the digit equal to sum of the prime factor. 666 = sum of the digits = 18, and prime factors 2, 3, 3, 37 and
666 /2 =33
#include <stdio.h>
#include <conio.h>
int prime(int);
int sep(int);
void main()
{
clrscr();
int n,num,s,sum=0,f,i;
printf("\nEnter a No : ");
scanf("%d",&n);
num=n;
s=sep(n);
f=0;
for(i=2;i<=n;)
{
if(n%i==0)
{
n=n/i;
f=prime(i);
if(f==0)
{
if(i<10)
sum=sum+i;
else
sum=sum+sep(i);
}
}
else
i++;
}
if(s==sum)
printf("\n %d is a Smith Number",n);
else
printf("\n %d is not a Smith Number",n);
getch();
}
int prime(int n)
{
int i;
for(i=2;i<=n/2;i++)
{
if(n%i==0)
return 1;
}
return 0;
}
int sep(int n)
{
int s=0;
while(n&glt;0)
{
s=s+n%10;
n=n/10;
}
return s;
}
Powerful No. is a number which divide by all its prime factors as well as square of it.
#include <stdio.h>
#include <conio.h>
int isprime(int n)
{
int i;
for(i=2;i<=n/2;i++)
{
if(n%i==0)
return 0;
}
return 1;
}
void main()
{
int i,j,f;
clrscr();
for(i=1;i<=150;i++)
{
f=1;
for(j=2;j<=i/2;j++)
{
if(i%j==0)
{
f=0;
if(isprime(j)==1)
{
if(i%(j*j)!=0)
{
f=1;
break;
}
}
}
}
if(f==0)
printf("%d ",i);
}
getch();
}
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