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

1,1

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..34.

Example

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.

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 *)

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, 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

Crossrefs

Subsequence of A006567 (emirps).

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

Sequence in context: A212948 A204471 A139778 * A178506 A248443 A254391

Adjacent sequences: A346022 A346023 A346024 * A346026 A346027 A346028

Keyword

nonn,base

Author

Lars Blomberg, Jul 02 2021

Status

approved