A353031 Emirps p such that both p and its digit reversal can be written as q*r+q+r where q and r are emirps.

134999, 999431, 1383947, 1903103, 3013091, 3626339, 7282487, 7493831, 7842827, 9336263, 9366839, 9386639, 9562499, 9942659, 11230199, 11370743, 11394431, 11650571, 11769839, 11884079, 13182623, 13413599, 13449311, 13611023, 13683179, 13881323, 15123527, 15788771, 15925391, 15934463, 17505611

Offset: 1

Author

J. M. Bergot and Robert Israel, Apr 18 2022

Keywords

• nonn
• base

Comments

Members of A352249 whose digit reversals are also in A352249.

Examples

			a(6) = 3626339 is a term because 3626339 = 37*95429 + 37 + 95429, its digit reversal 9336263 = 97*95267 + 97 + 95267, and 3626339, 37, 95429, 97 and 95267 are all emirps.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A004086, A006567, A352249.

Programs

Maple

revdigs:= proc(n) local L, i; L:= convert(n, base, 10); add(L[-i]*10^(i-1), i=1..nops(L)) end proc:
isemirp:= proc(p) local r;
   if not isprime(p) then return false fi;
   r:= revdigs(p);
   r <> p and isprime(r)
end proc:
filter:= proc(p) local q,t,flag;
  if not isprime(p) then return false fi;
  q:= revdigs(p);
  if q=p or not isprime(q) then return false fi;
  flag:= false;
for t in select(`<`, numtheory:-divisors(p+1),floor(sqrt(p+1))) do
  if isemirp(t-1) and isemirp((p+1)/t-1) then flag:= true; break fi
od;
if not flag then return false fi;
for t in select(`<`, numtheory:-divisors(q+1),floor(sqrt(q+1))) do
     if isemirp(t-1) and isemirp((q+1)/t-1) then return true fi
od;
false
end proc:
p:= 2: R:= NULL: count:= 0:
while count < 40 do
  p:= nextprime(p);
d:=  ilog10(p);
p1:= floor(p/10^d);
  if p1=2 then p:= nextprime(3*10^d)
  elif member(p1,{4,5,6}) then p:= nextprime(7*10^d)
  elif p1=8 then p:= nextprime(9*10^d)
fi;
  if filter(p) then R:= R, p; count:= count+1 fi;
od:
R;