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A213883 Least number k such that (10^k-j)*10^n-1 is prime for some single-digit j or 0 if no such prime with 1<=k, 0<=j<=9 exists. 4
1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 3, 2, 1, 1, 3, 5, 5, 3, 1, 3, 3, 1, 1, 9, 1, 1, 1, 1, 1, 7, 3, 6, 4, 1, 4, 4, 1, 15, 10, 1, 7, 3, 1, 3, 2, 2, 4, 6, 1, 3, 5, 20, 1, 1, 1, 8, 10, 7, 15, 10, 1, 4, 2, 5, 8, 3, 23, 11, 2, 2, 9, 3, 1, 5, 4, 1, 6, 3, 18, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,9

COMMENTS

j cannot be 0, 3, 6 or 9 because we are searching for repdigit primes with k-1 times the digit 9, one digit (9-j), and n least-significant digits 9 (so n+k-1 times the digit 9 in total). If j is a multiple of 3, that number is also a multiple of 3 and not prime.

Conjecture: there is always at least one (k,j) solution for each n.

LINKS

Pierre CAMI, Table of n, a(n) for n = 1..2200

EXAMPLE

Refers to the primes 89, 599, 8999, 79999, 799999, 4999999, 89999999,...

MAPLE

A213883 := proc(n)

    for k from 1 to 2*n-1 do

        for j from 0 to 9 do

            if isprime( (10^k-j)*10^n-1) then

                return k;

            end if;

        end do:

    end do:

    return 0 ;

end proc: # R. J. Mathar, Jul 20 2012

PROG

SCRIPT

DIM nn, 0

DIM jj

DIM kk

DIMS tt

OPENFILEOUT myfile, a(n).txt

LABEL loopn

SET nn, nn+1

IF nn>2200 THEN END

SET kk, 0

LABEL loopk

SET kk, kk+1

IF kk>2*nn THEN GOTO loopn

SET jj, 0

LABEL loopj

SET jj, jj+1

IF jj%3==0 THEN SET jj, jj+1

IF jj>9 THEN GOTO loopk

SETS tt, %d, %d, %d\,; nn; kk; jj

PRP (10^kk-jj)*10^nn-1, tt

IF ISPRP THEN GOTO a

IF ISPRIME THEN GOTO a

GOTO loopj

LABEL a

WRITE myfile, tt

GOTO loopn

CROSSREFS

Cf. A213790, A213884 (corresponding j).

Sequence in context: A230517 A165003 A165011 * A192190 A272729 A064034

Adjacent sequences:  A213880 A213881 A213882 * A213884 A213885 A213886

KEYWORD

nonn

AUTHOR

Pierre CAMI, Jun 26 2012

STATUS

approved

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Last modified February 23 15:57 EST 2020. Contains 332170 sequences. (Running on oeis4.)