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A228629 Members p of a pair of primes (p,q) such that the decimal digits of q are the 9's complement of the decimal digits of p.

%I A228629 #16 Oct 06 2020 19:28:47
%S A228629 2,7,23,61,67,83,107,109,127,163,167,181,211,223,227,239,241,251,263,
%T A228629 269,271,277,283,293,307,367,383,389,401,409,421,461,463,467,487,509,
%U A228629 521,523,563,587,601,607,613,617,631,641,643,647,653,661,673,677,683,701
%N A228629 Members p of a pair of primes (p,q) such that the decimal digits of q are the 9's complement of the decimal digits of p.
%C A228629 We consider length(p) = length(q). For example, the primes p = 97, 997, 99999999999999997,...(see A003618) are not in the sequence with q = 2.
%C A228629 Each prime p appears only once in the sequence, but the pair (p, q) is not unique, for example the prime 163 generates two pairs of primes(163, 683) and (163, 863), the prime 283 generates three pairs of primes(283, 167), (283, 617) and (283, 761).
%C A228629 The couples of primes (p, q) are (2, 7), (7, 2), (23, 67), (61, 83), (67, 23), (83, 61), (107, 829), (109, 809), (127, 827),...
%C A228629 In the general case, the digits of p are different from q, but there exists numbers p such that q has the same digits as p, for example (p, q) = (227, 277), (727, 227), (881, 181), ...
%H A228629 Robert Israel, <a href="/A228629/b228629.txt">Table of n, a(n) for n = 1..10000</a>
%e A228629 23 is in the sequence because 9-2 = 7 and 9 - 3 = 6 => 67 is prime, and we obtain the pair (23, 67).
%p A228629 with(numtheory):kk:=0:
%p A228629     for n from 1 to 200 do:
%p A228629       ii:=0:
%p A228629         for k from 1 to 2000 while(ii=0) do:
%p A228629         p1:=ithprime(n):p2:=ithprime(k):
%p A228629         x1:=convert(p1,base,10):n1:=nops(x1):
%p A228629         x2:=convert(p2,base,10):n2:=nops(x2):
%p A228629          if n1=n2 then
%p A228629          W:=array(1..n1):U:=array(1..n1):U1:=array(1..n1):
%p A228629            for c from 1 to n1 do:
%p A228629            U1[c]:=x1[c]:od:U:=sort(x1,`<`):V:=sort(x2,`>`):
%p A228629              for j from 1 to n1 do:
%p A228629              W[j]:= 9-V[j]:od:W1:=sort(W,`>`):jj:=0:
%p A228629                for b from 1 to n1 do:
%p A228629                  if U[b]=W1[b] then
%p A228629                  jj:=jj+1:
%p A228629                  else fi:
%p A228629                od:
%p A228629                  if jj=n1 then
%p A228629                   ii:=1: kk:=kk+1: printf(`%d, `,p1):
%p A228629                   else
%p A228629                  fi:
%p A228629            fi:
%p A228629         od:
%p A228629        od:
%p A228629 # Alternative:
%p A228629 R:= 2,7:
%p A228629 for d from 2 to 3 do
%p A228629   P:= select(isprime,[seq(i,i=10^(d-1)+1..10^d-1,2)]);
%p A228629   nP:= nops(P);
%p A228629   Pd:= map(sort@convert,P,base,10);
%p A228629   Ps:= convert(map(t -> ListTools:-Reverse([9$d]-t), Pd),set);
%p A228629   S:= select(t -> member(Pd[t],Ps),[$1..nP]);
%p A228629   R:= R, op(P[S]);
%p A228629 od:
%p A228629 R; # _Robert Israel_, Oct 06 2020
%Y A228629 Cf. A228628.
%K A228629 nonn,base
%O A228629 1,1
%A A228629 _Michel Lagneau_, Aug 28 2013