A353030
a(n) is the first emirp p such that there are exactly n unordered pairs (q,r) of emirps with p = q*r + q + r.
Original entry on oeis.org
13, 1439, 100799, 3548879, 14061599, 38342303, 120355199, 12555446399
Offset: 0
a(3) = 3548879 because 3548879 = 17*197159 + 17 + 197159 = 359*9857 + 359 + 9857 = 953*3719 + 953 + 3719 and 3548879, 17, 197159, 359, 9857, 953, 3719 are emirps.
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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:
g:= proc(n) local p,q, t,count;
count:= 0;
for t in select(`<`,numtheory:-divisors(n+1),floor(sqrt(n+1))) do
if isemirp(t-1) and isemirp((n+1)/t-1) then
count:= count+1;
fi
od;
count
end proc:
V:= Array(0..6): vcount:= 0:
p:= 2:
while vcount < 7 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 isemirp(p) then
v:= g(p);
if V[v] = 0 then vcount:= vcount+1; V[v]:= p; fi;
fi
od:
convert(V,list);
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.
Original entry on oeis.org
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
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.
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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;
Showing 1-2 of 2 results.
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