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A345528
a(n) is the first prime that begins a sequence of exactly n consecutive primes that are emirps.
0
97, 13, 71, 733, 3371, 10039, 11897, 334759, 7904639, 1193, 1477271183, 9387802769, 15423094826093
OFFSET
1,1
COMMENTS
The prime before a(n) is not an emirp, the n consecutive primes starting with a(n) are emirps, and the next prime is not an emirp.
a(n) > 2*10^8 for n > 10.
EXAMPLE
a(3) = 71 because the 3 consecutive primes 71, 73, 79 are emirps while the previous and next primes 67 and 83 are not emirps.
MAPLE
digrev:= proc(n) local L, i;
L:= convert(n, base, 10);
add(L[-i]*10^(i-1), i=1..nops(L))
end proc:
isemirp:= proc(n) local r;
r:= digrev(n);
r <> n and isprime(r)
end proc:
V:= Vector(10): count:= 0:
p:= 2: ep:= 0: q:= 2:
while count < 10 do
p:= nextprime(p);
flag:= isemirp(p);
if flag then
if ep = 0 then q:= p fi;
ep:= ep+1;
else
if ep > 0 then
if ep <= 10 and V[ep] = 0 then
count:= count+1; V[ep]:= q;
fi;
fi;
ep:= 0;
fi
od:
convert(V, list);
CROSSREFS
KEYWORD
nonn,more,base
AUTHOR
J. M. Bergot and Robert Israel, Jun 20 2021
EXTENSIONS
a(11)-a(12) from Daniel Suteu, Jun 21 2021
a(13) from Martin Ehrenstein, Jun 28 2021
STATUS
approved