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A056730 Palindromic primes with just two distinct digits.

%I A056730 #14 Sep 12 2018 01:12:55
%S A056730 101,131,151,181,191,313,353,373,383,727,757,787,797,919,929,11311,
%T A056730 11411,13331,15551,16661,18181,19991,32323,33533,35353,72227,72727,
%U A056730 74747,75557,76667,77377,77477,77977,78787,78887,79997,94949,95959
%N A056730 Palindromic primes with just two distinct digits.
%H A056730 Robert Israel, <a href="/A056730/b056730.txt">Table of n, a(n) for n = 1..10000</a>
%p A056730 f:= proc(d) local d1,d2,L,cand,C1,C2,C3,a,b,n,Cands;
%p A056730     Cands:= NULL;
%p A056730     d1:= (d+1)/2;
%p A056730     d2:= d-d1;
%p A056730     for b in [1,3,7,9] do
%p A056730       for a in {$0..9} minus {b} do
%p A056730         for n from 2^(d1-1) to 2^d1-2 do
%p A056730           L:= convert(n,base,2);
%p A056730           C1:= a*(10^d-1)/9;
%p A056730           C2:= (b-a)*add(L[i]*10^(i+d2-1),i=1..d1);
%p A056730           C3:= (b-a)*add(L[i]*10^(d1-i),i=2..d1);
%p A056730           cand:= C1+C2+C3;
%p A056730           if isprime(cand) then Cands:= Cands, cand; fi
%p A056730     od od od;
%p A056730     sort([Cands])
%p A056730 end proc:
%p A056730 map(op, [seq(f(d),d=3..7,2)]); # _Robert Israel_, Sep 09 2018
%t A056730 Select[ Range[ 1, 3 10^6, 2 ], PrimeQ[ # ] && Length[ Union[ RealDigits[ # ][ [ 1 ] ] ] ] == 2 && RealDigits[ # ][ [ 1 ] ] == Reverse[ RealDigits[ # ][ [ 1 ] ] ] & ]
%Y A056730 Intersection of A002385 and A031955.
%K A056730 nonn,base
%O A056730 1,1
%A A056730 _Robert G. Wilson v_, Aug 11 2000