A213886 Number of prime numbers of the form (10^k-j)*10^n-1 with 0<k<=2*n and 0<j<9.

7, 7, 11, 10, 15, 7, 10, 13, 19, 13, 10, 11, 9, 16, 10, 7, 10, 9, 15, 13, 17, 17, 18, 4, 10, 14, 7, 11, 8, 12, 16, 15, 18, 10, 17, 8, 12, 8, 6, 13, 7, 9, 15, 8, 12, 10, 18, 5, 3, 11, 18, 9, 18, 14, 10, 13, 15, 13, 12, 8, 11, 8, 10, 8

Offset

1,1

Comments

The condition k<=2*n means we are setting an upper limit to the set of numbers to be checked given some n.

The condition 0<j<9 says we are only interested in near repdigit 9 primes, in practice only j = 1, 2, 4, 5, 7 or 8 seem to occur.

Statistics of entries over the range n=1 to 1000: all a(n) are > 0, with a minimum of 3 and a maximum of 27. The average of the a(n) is 12.

Links

Pierre CAMI, Table of n, a(n) for n = 1..1000

Example

a(1)=7 counts 89, 79, 59, 29, 19, 929 and 919.
a(2)=7 counts 599, 499, 199, 9199, 999599, 999499 and 999199.

Maple

A213886 := proc(n)
    local a, k, j;
    a := 0 ;
    for k from 1 to 2*n do
        for j from 1 to 8 do
            if isprime((10^k-j)*10^n-1) then
                a := a+1 ;
            end if;
        end do:
    end do:
    return a;
end proc: # R. J. Mathar, Jul 19 2012

Prog

(PFGW64 and SCRIPTIFY)
SCRIPT
DIM nn, 0
DIM kk
DIM jj
DIM cc, 0
DIMS tt
OPENFILEOUT myfile, a(n).txt
LABEL loopn
SET nn, nn+1
IF nn>1000 THEN END
SET cc, 0
SET kk, 0
LABEL loopk
SET kk, kk+1
IF kk>2*nn THEN GOTO a
SET jj, 9
LABEL loopj
SET jj, jj-1
IF jj%3==0 THEN SET jj, jj-1
IF jj<0 THEN GOTO loopk
SETS tt, %d, %d\,; nn; cc
PRP (10^kk-jj)*10^nn-1, tt
IF ISPRP THEN SET cc, cc+1
IF ISPRIME THEN SET cc, cc+1
GOTO loopj
LABEL a
WRITE myfile, tt
GOTO loopn

Crossrefs

Cf. A213885

Sequence in context: A084513 A084523 A336019 * A053673 A204910 A152672

Adjacent sequences: A213883 A213884 A213885 * A213887 A213888 A213889

Keyword

nonn

Author

Pierre CAMI, Jul 10 2012

Status

approved