A224502 Prime numbers (together with one) whose representation in balanced ternary are palindromes.

1, 7, 13, 43, 61, 73, 103, 367, 421, 457, 547, 601, 613, 757, 859, 1039, 1093, 3823, 4021, 4561, 4723, 4759, 5743, 6211, 6373, 6481, 6949, 7219, 7489, 7933, 8563, 8941, 9103, 9679, 29527, 30013, 31147, 31741, 33037, 35251, 36061, 36097, 36583, 37717, 39607, 41011, 42667, 43963, 44773, 45691, 47581, 49201

Offset: 1

Author

Malachi de Ælfweald, Apr 08 2013

Keywords

• nonn
• base

Comments

Intersection of A006005 and A134027.

Examples

			For n=5, a(5)=61 and in balanced ternary notation is 1ī1ī1.
		

Links

• Malachi de Ælfweald and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 199 terms from Malachi de Ælfweald)
• Wikipedia, Balanced ternary

Programs

PARI

bt(k,n)={
    sum(i=0,(n-1)\2,
        my(t=k%3-1);
        k\=3;
        n--;
        if(n==i,3^n,3^i+3^n)*t
    )
};
do(N)={
    my(v=List([1]),t);
    for(n=1,N,
        forstep(k=2,3^((n+1)\2)-1,3,
            t=bt(k,n);
            if(isprime(t),listput(v,t))
        )
    );
    vecsort(Vec(v))
}; \\ Charles R Greathouse IV, Apr 08 2013