A213882 Numbers b such that there is at least one number c and one single-digit number d such that (10^c-d)*10^b-1 and (10^c-d)*10^b+1 are twin primes with 0 < c < 2*b.

1, 2, 3, 4, 5, 6, 7, 8, 9, 13, 14, 15, 19, 21, 23, 26, 40, 43, 45, 52, 54, 55, 69, 77, 90, 99, 106, 128, 147, 176, 202, 267, 331, 458, 512, 555, 908, 942, 1004, 1123, 1374, 1386, 1467

Offset: 1

Author

Pierre CAMI, Jun 26 2012

Keywords

• nonn

Comments

The single-digit number d is always 1, 4, or 7 in this format because otherwise one of (10^c-d)*10^b+-1 is a multiple of 3.

For one b there may be more than one matching (c,d).

The sequence of associated minimum c values starts: 1, 1, 1, 2, 3, 6, 1, 4, 2, 11, 9, 4, 7, 12, 9, 9, 42, 62, 5, 31, 2, 72, 88, 141, 119, 181, 6, 38, 164, 132, 53, 293, 150, 704, 557, 980, 952, 1596, 529, 2221, 200, 169, 1371,... and their associated d values are 4, 4, 1, 1, 1, 1, 7, 4, 7, 4, 1, 1, 4, 1, 7, 1, 4, 1, 7, 7, 7, 4, 1, 7, 1, 7, 4, 4, 4, 7, 1, 1, 7, 7, 4, 4, 4, 1, 1, 7, 7, 1, 1, ....

Examples

			(10^1-7)*10^1-1=29 prime 31 the twin prime so a(1)=1.
(10^1-4)*10^2-1=599 prime 601 the twin prime so a(2)=2.
(10^1-1)*10^3-1=8999 prime 9001 the twin prime so a(3)=3.
(10^2-1)*10^4-1=989999 prime 990001 twin prime so a(4)=4.
(10^3-1)*10^5-1=99899999 prime.
(10^3-1)*10^5+1=99900001 twin prime so a(5)=5.
		

Crossrefs

Cf. A213883, A213884.

Programs

Maple

isA213882 := proc(b)
     local c,d,p;
    for c from 1 to 2*b-1 do
        for d from 0 to 9 do
            p := (10^c-d)*10^b-1 ;
            if isprime(p) and isprime(p+2) then
                return true;
            end if;
        end do:
    end do:
    return false ;
end proc:
for n from 1 to 2000 do
    if isA213882(n) then
        printf("%d,\n",n);
    end if;
end do; # R. J. Mathar, Jul 21 2012