A346022 Primes that are the first in a run of exactly 2 emirps.

13, 31, 337, 701, 761, 937, 983, 1151, 1279, 1831, 1933, 3191, 3803, 3851, 3911, 7043, 7219, 7457, 7523, 7643, 9127, 9161, 9241, 9437, 9521, 9547, 9601, 9871, 9931, 10007, 10151, 10247, 10487, 10639, 10853, 10889, 11071, 11657, 11833, 12071, 12547, 12689

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..42.

Example

a(2) = 31 because of the four consecutive primes 29, 31, 37, 41 only 31, 37 are emirps.

Prog

(Python)
from sympy import isprime, nextprime
def isemirp(p): s = str(p); return s != s[::-1] and isprime(int(s[::-1]))
def aupto(limit):
  alst, pvec, evec, p = [], [2, 3, 5, 7], [0, 0, 0, 0], 11
  while pvec[1] <= limit:
    if evec == [0, 1, 1, 0]: alst.append(pvec[1])
    pvec = pvec[1:] + [p]; evec = evec[1:] + [isemirp(p)]; p = nextprime(p)
  return alst
print(aupto(12689)) # Michael S. Branicky, Jul 04 2021

Crossrefs

Subsequence of A006567 (emirps).

Cf. A003684, A048052, A048054, A071612.

Sequence in context: A299888 A023304 A247837 * A227172 A180757 A214488

Adjacent sequences: A346019 A346020 A346021 * A346023 A346024 A346025

Keyword

nonn,base

Author

Lars Blomberg, Jul 01 2021

Status

approved