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 A 3-digit number (Posted on 2018-10-27)
What is the smallest palindromic prime whose cube can be expressed as the sum of three odd cubes ?

 No Solution Yet Submitted by Ady TZIDON No Rating

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 computer soln | Comment 1 of 9
I wonder if 3 is palindromic. If not, 757 fits the bill as below:

rabbit-3:~ lord\$ t3

3 =    1^3    +     1^3    +     1^3

757 =    1^3    +     3^3    +     9^3

16561 =   13^3    +    13^3    +    23^3

73037 =   19^3    +    19^3    +    39^3

77977 =   13^3    +    19^3    +    41^3

rabbit-3:~ lord\$ more t3.f

program t3

implicit none

integer*8 y3(1000000,4),num(8),i1,i2,i3,icnt,

1 i,j,ndig,n,dum,half

icnt=0

do i1=1,101,2

do i2=i1,101,2

do i3=i2,101,2

icnt=icnt+1

y3(icnt,4)=i1**3+i2**3+i3**3

y3(icnt,1)=i1

y3(icnt,2)=i2

y3(icnt,3)=i3

enddo

enddo

enddo

do 1 i=3,icnt,2

call isprime(i,n)

if (n.eq.0)go to 1

ndig=log10(1.*i)+1

dum=i

do j=ndig-1,1,-1

num(j+1)=dum/10**j

dum=dum-num(j+1)*10**j

enddo

num(1)=dum

half=(ndig+1)/2

do j=1,half

if(num(j).ne.num(ndig+1-j))go to 1

enddo

do j=1,1000000

if(y3(j,4).ne.i)go to 2

print 3,i,y3(j,1),y3(j,2),y3(j,3)

3               format(i6, ' =',2(2x,i3,'^3    + '),2x,i3,'^3')

2               enddo

1          enddo

end

subroutine isprime(i,n)

implicit none

integer*8 i,j,k,l,m,n

n=1

if(i.eq.2)return

n=0

k=sqrt(1.*i)

do j=2,k

m=(1.*i)/(1.*j)

l=m*j

if(l.eq.i)go to 1

enddo

n=1

1       return

end

Edited on October 27, 2018, 11:58 am
 Posted by Steven Lord on 2018-10-27 09:19:38

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