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

733, 7177, 9011, 11551, 11777, 12107, 13147, 13259, 13693, 14563, 19219, 19531, 19661, 31891, 32467, 35117, 35311, 36097, 36187, 38351, 38903, 70241, 70921, 75721, 77323, 78607, 79399, 79531, 90121, 91183, 92297, 92479, 92959, 93581, 94121, 95111, 95791, 96857

Offset

1,1

Comments

There are large gaps in this sequence because all terms need to begin with 1, 3, 7, or 9 otherwise the reversal is composite.

Links

Table of n, a(n) for n=1..38.

Example

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.

Mathematica

Select[Prime@Range@10000, Boole[PrimeQ@#&&!PalindromeQ@#&/@(IntegerReverse/@NextPrime[#, Range[-1, 4]])]=={0, 1, 1, 1, 1, 0}&] (* Giorgos Kalogeropoulos, Jul 04 2021 *)

Prog

(Python)
from sympy import isprime, primerange
def isemirp(p): s = str(p); return s != s[::-1] and isprime(int(s[::-1]))
def aupto(limit):
    alst, pvec, evec = [], [2, 3, 5, 7, 11, 13], [0, 0, 0, 0, 0, 0]
    for p in primerange(17, limit+1):
        if evec == [0, 1, 1, 1, 1, 0]: alst.append(pvec[1])
        pvec = pvec[1:] + [p]; evec = evec[1:] + [isemirp(p)]
    return alst
print(aupto(97000)) # Michael S. Branicky, Jul 04 2021

Crossrefs

Subsequence of A006567 (emirps)

Cf. A003684, A048052, A048054, A071612, A346022, A346023, A346025.

Sequence in context: A143726 A180919 A166607 * A297761 A220625 A260035

Adjacent sequences: A346021 A346022 A346023 * A346025 A346026 A346027

Keyword

nonn,base

Author

Lars Blomberg, Jul 02 2021

Status

approved