A215932 Happy reversible primes.

7, 13, 31, 79, 97, 167, 313, 383, 709, 739, 761, 907, 937, 1009, 1033, 1151, 1487, 1511, 1733, 1847, 1933, 3019, 3067, 3083, 3109, 3301, 3319, 3371, 3391, 3463, 3643, 3803, 7457, 7481, 7547, 7589, 7603, 7841, 9001, 9013, 9103, 9133, 9857, 10009, 10039, 10067

Offset: 1

Author

Jayanta Basu, Mar 16 2013

Keywords

• nonn
• base

Comments

Happy numbers that are prime and if the digits are reversed they remain prime (and of course happy, since addition is commutative).

Intersection of A007500 and A007770. - N. J. A. Sloane, Mar 16 2013

This is to A031161 (palindromic lucky numbers) as prime happy numbers are to lucky numbers (A000959). - Jonathan Vos Post, Mar 16 2013

Crossrefs

Cf. A007500, A007770, A035497.

Programs

C

int main()
{long unsigned int n,i,si,a[]={4,16,37,58,89,145,42,20},t,x,c1=0, sod(long unsigned int),rev(long unsigned int),prim(long unsigned int);
for(n=2;n<=12000;n++) {t=n;si=0;while(si!=1){for(i=0;i<=7;i++){if(t==a[i]){si=1;break;}}
                        if(t==1){si=1;if(prim(n)==0){x=rev(n);if(prim(x)==0){printf(", %lu",n);c1=c1+1;}}}t=sod(t);}}}
long unsigned int sod(long unsigned int m){long unsigned int d=0,r;while(m>0){r=m%10;d=d+r*r;m=m/10;} return(d);}
long unsigned int rev(long unsigned int p){long unsigned int d=0,r;while(p>0){r=p%10;d=d*10+r;p=p/10;}return(d);}
long unsigned int prim(long unsigned int n){long unsigned int i,d=0; for(i=2;i<=n/2;i++){if(n%i==0){d=1;break;}}return(d);}

Mathematica

revpQ[n_] := PrimeQ[n] && PrimeQ[FromDigits@Reverse@IntegerDigits@n]; happyQ[n_] := Block[{w = n}, While[w > 6, w = Total[ IntegerDigits[w]^2]]; w == 1]; Select[Range[10^4], revpQ[#] && happyQ[#] &] (* Giovanni Resta, Mar 16 2013 *)