A346025 Primes that are the first in a run of exactly 5 emirps.

3371, 9769, 11699, 11953, 15493, 34549, 72307, 72547, 105653, 106391, 109849, 129587, 139387, 144407, 169067, 170759, 178333, 193261, 193877, 316073, 324031, 324893, 325163, 333923, 339671, 375787, 381859, 389287, 701383, 701593, 712289, 722633, 744377, 777349

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) = 3371 because of the seven consecutive primes 3361, 3371, 3373, 3389, 3391, 3407, 3413 all except 3361 and 3413 are emirps and this is the first such occurrence.
		

Crossrefs

Subsequence of A006567 (emirps).

Cf. A003684, A048052, A048054, A071612, A346022, A346023, A346024.

Programs

Mathematica

Select[Prime@Range@20000,Boole[PrimeQ@#&&!PalindromeQ@#&/@(IntegerReverse/@NextPrime[#,Range[-1,5]])]=={0,1,1,1,1,1,0}&] (* 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, 13, 17], [0, 0, 0, 0, 0, 0, 0]
    for p in primerange(19, limit+1):
        if evec == [0, 1, 1, 1, 1, 1, 0]: alst.append(pvec[1])
        pvec = pvec[1:] + [p]; evec = evec[1:] + [isemirp(p)]
    return alst
print(aupto(780000)) # Michael S. Branicky, Jul 04 2021