cp's OEIS Frontend

A346024 Primes that are the first in a run of exactly 4 emirps.

%I A346024 #10 Jul 04 2021 16:02:15
%S A346024 733,7177,9011,11551,11777,12107,13147,13259,13693,14563,19219,19531,
%T A346024 19661,31891,32467,35117,35311,36097,36187,38351,38903,70241,70921,
%U A346024 75721,77323,78607,79399,79531,90121,91183,92297,92479,92959,93581,94121,95111,95791,96857
%N A346024 Primes that are the first in a run of exactly 4 emirps.
%C A346024 There are large gaps in this sequence because all terms need to begin with 1, 3, 7, or 9 otherwise the reversal is composite.
%e A346024 a(1) = 733 because of the six consecutive primes 727, 733, 739, 743, 751, 757 all except 727 and 757 are emirps and this is the first such occurrence.
%t A346024 Select[Prime@Range@10000,Boole[PrimeQ@#&&!PalindromeQ@#&/@(IntegerReverse/@NextPrime[#,Range[-1,4]])]=={0,1,1,1,1,0}&] (* _Giorgos Kalogeropoulos_, Jul 04 2021 *)
%o A346024 (Python)
%o A346024 from sympy import isprime, primerange
%o A346024 def isemirp(p): s = str(p); return s != s[::-1] and isprime(int(s[::-1]))
%o A346024 def aupto(limit):
%o A346024     alst, pvec, evec = [], [2, 3, 5, 7, 11, 13], [0, 0, 0, 0, 0, 0]
%o A346024     for p in primerange(17, limit+1):
%o A346024         if evec == [0, 1, 1, 1, 1, 0]: alst.append(pvec[1])
%o A346024         pvec = pvec[1:] + [p]; evec = evec[1:] + [isemirp(p)]
%o A346024     return alst
%o A346024 print(aupto(97000)) # _Michael S. Branicky_, Jul 04 2021
%Y A346024 Subsequence of A006567 (emirps)
%Y A346024 Cf. A003684, A048052, A048054, A071612, A346022, A346023, A346025.
%K A346024 nonn,base
%O A346024 1,1
%A A346024 _Lars Blomberg_, Jul 02 2021