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

Author

Lars Blomberg, Jul 02 2021

Keywords

• nonn
• base

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.

Examples

			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.
		

Crossrefs

Subsequence of A006567 (emirps)

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

Programs

Mathematica

Select[Prime@Range@10000,Boole[PrimeQ@#&&!PalindromeQ@#&/@(IntegerReverse/@NextPrime[#,Range[-1,3]])]=={0,1,1,1,0}&] (* Giorgos Kalogeropoulos, Jul 04 2021 *)

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