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, ....
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
KEYWORD
nonn
AUTHOR
Pierre CAMI, Jun 26 2012
STATUS
approved