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

Author

Lars Blomberg, Jul 01 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(2) = 31 because of the four consecutive primes 29, 31, 37, 41 only 31, 37 are emirps.
		

Crossrefs

Subsequence of A006567 (emirps).

Cf. A003684, A048052, A048054, A071612.

Programs

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