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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. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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, ....

LINKS

Table of n, a(n) for n=1..43.

EXAMPLE

(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.

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

CROSSREFS

Cf. A213883, A213884.

Sequence in context: A247811 A007377 A305932 * A135140 A052061 A045540

Adjacent sequences:  A213879 A213880 A213881 * A213883 A213884 A213885

KEYWORD

nonn

AUTHOR

Pierre CAMI, Jun 26 2012

STATUS

approved

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Last modified May 17 10:16 EDT 2022. Contains 353745 sequences. (Running on oeis4.)