A056730 Palindromic primes with just two distinct digits.

101, 131, 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, 797, 919, 929, 11311, 11411, 13331, 15551, 16661, 18181, 19991, 32323, 33533, 35353, 72227, 72727, 74747, 75557, 76667, 77377, 77477, 77977, 78787, 78887, 79997, 94949, 95959

Offset: 1

Author

Robert G. Wilson v, Aug 11 2000

Keywords

• nonn
• base

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A002385 and A031955.

Programs

Maple

f:= proc(d) local d1,d2,L,cand,C1,C2,C3,a,b,n,Cands;
    Cands:= NULL;
    d1:= (d+1)/2;
    d2:= d-d1;
    for b in [1,3,7,9] do
      for a in {$0..9} minus {b} do
        for n from 2^(d1-1) to 2^d1-2 do
          L:= convert(n,base,2);
          C1:= a*(10^d-1)/9;
          C2:= (b-a)*add(L[i]*10^(i+d2-1),i=1..d1);
          C3:= (b-a)*add(L[i]*10^(d1-i),i=2..d1);
          cand:= C1+C2+C3;
          if isprime(cand) then Cands:= Cands, cand; fi
    od od od;
    sort([Cands])
end proc:
map(op, [seq(f(d),d=3..7,2)]); # Robert Israel, Sep 09 2018

Mathematica

Select[ Range[ 1, 3 10^6, 2 ], PrimeQ[ # ] && Length[ Union[ RealDigits[ # ][ [ 1 ] ] ] ] == 2 && RealDigits[ # ][ [ 1 ] ] == Reverse[ RealDigits[ # ][ [ 1 ] ] ] & ]