A346023 Primes that are the first in a run of exactly 3 emirps.

71, 953, 1021, 1097, 1381, 1499, 1583, 1723, 3011, 3083, 3271, 3343, 3463, 7673, 7949, 9209, 9479, 10453, 10987, 11149, 12289, 12743, 13499, 13751, 14057, 14087, 14549, 15289, 15649, 15731, 16103, 16193, 16567, 17033, 17203, 17669, 17737, 17903, 18899, 19793

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..40.

Example

a(1) = 71 because of the five consecutive primes 67, 71, 73, 79, 83 all except 67 and 83 are emirps and this is the first such occurrence.

Mathematica

Select[Prime@Range@10000, Boole[PrimeQ@#&&!PalindromeQ@#&/@(IntegerReverse/@NextPrime[#, Range[-1, 3]])]=={0, 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], [0, 0, 0, 0, 0]
    for p in primerange(13, limit+1):
        if evec == [0, 1, 1, 1, 0]: alst.append(pvec[1])
        pvec = pvec[1:] + [p]; evec = evec[1:] + [isemirp(p)]
    return alst
print(aupto(20000)) # Michael S. Branicky, Jul 04 2021

Crossrefs

Subsequence of A006567 (emirps)

Cf. A003684, A048052, A048054, A071612, A346022, A346024, A346025.

Sequence in context: A393685 A253683 A210699 * A389721 A050885 A200909

Adjacent sequences: A346020 A346021 A346022 * A346024 A346025 A346026

Keyword

nonn,base

Author

Lars Blomberg, Jul 02 2021

Status

approved