A228629 -id:A228629 - cp's OEIS frontend

A338018 Primes not in A228629.

3, 5, 11, 13, 17, 19, 29, 31, 37, 41, 43, 47, 53, 59, 71, 73, 79, 89, 97, 101, 103, 113, 131, 137, 139, 149, 151, 157, 173, 179, 191, 193, 197, 199, 229, 233, 257, 281, 311, 313, 317, 331, 337, 347, 349, 353, 359, 373, 379, 397, 419, 431, 433, 439, 443, 449, 457, 479, 491, 499, 503, 541, 547, 557

Offset: 1

Robert Israel, Oct 06 2020

Primes p such that there is no prime whose decimal digits are (in some order) the 9's complements of the decimal digits of p.

Leading zeros are not allowed.

			a(4)=13 is a member because the 9's complements of the digits 1,3 are 8,2, and none of the integers 28 or 82 is prime.
a(26)=149 is a member because the 9's complements of its digits are 8,5,0, and none of the integers with those digits is prime.

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

Cf. A228629. Contains all members of A030096 except 7.

R:= 3,5:
for d from 2 to 4 do
  P:= select(isprime,[seq(i,i=10^(d-1)+1..10^d-1,2)]);
  nP:= nops(P);
  Pd:= map(sort@convert,P,base,10);
  Ps:= convert(map(t -> ListTools:-Reverse([9$d]-t), Pd),set);
  S:= remove(t -> member(Pd[t],Ps),[$1..nP]);
  R:= R, op(P[S]);
od:
R; # Robert Israel, Oct 06 2020

A185250 Array A(n,k), n > 0, k = 1,2 read by rows such that (A(n,1), A(n,2)) are the pairs of primes (p, q), p < q, where the decimal digits of q are the 9's complement of the decimal digits of p.

Original entry on oeis.org

2, 7, 23, 67, 61, 83, 107, 829, 109, 809, 127, 827, 163, 683, 163, 863, 167, 283, 167, 823, 181, 881, 211, 887, 223, 677, 227, 277, 227, 727, 239, 607, 241, 587, 241, 857, 251, 487, 263, 367, 263, 673, 269, 307, 271, 827, 283, 617, 283, 761, 293, 607, 383, 661

Offset: 1

Michel Lagneau, Aug 29 2013

The prime p in the pair (p, q) is not unique; for example, the prime 163 generates two pairs of primes: (163, 683) and (163, 863).

			(241, 587) and (241, 857) are in the sequence because the digits 5, 8, 7  are the 9's complement of the decimal digits of 241.

Michel Lagneau, Table of (p, q) for 5000 pairs

Cf. A228629.

with(numtheory):
     for n from 1 to 200 do:
        p1:=ithprime(n)
         for k from n+1 to 2000 do:
          p2:=ithprime(k):
          x1:=convert(p1,base,10):n1:=nops(x1):
          x2:=convert(p2,base,10):n2:=nops(x2):
            if n1=n2 then
            W:=array(1..n1):U:=array(1..n1):U1:=array(1..n1):
              for c from 1 to n1 do:
              U1[c]:=x1[c]:od:U:=sort(x1,`<`):V:=sort(x2,`>`):
                 for j from 1 to n1 do:
                   W[j]:= 9-V[j]:od:W1:=sort(W,`>`):jj:=0:
                     for b from 1 to n1 do:
                     if U[b]=W1[b] then jj:=jj+1:
                     else
                     fi:
                     od:
                     if jj=n1 and p1

cp's OEIS Frontend

A338018 Primes not in A228629.

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