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.

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

1,1

Comments

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).

Links

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

Example

(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.

Maple

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<p2
                     then
                     printf(`%d, `, p1):
                     printf(`%d, `, p2):else
                     fi:
              fi:
           od:
         od:

Crossrefs

Cf. A228629.

Sequence in context: A228629 A010748 A272819 * A048496 A369840 A210581

Adjacent sequences: A185247 A185248 A185249 * A185251 A185252 A185253

Keyword

nonn,base,less

Author

Michel Lagneau, Aug 29 2013

Status

approved