A346022 - OEIS

%I #14 Jul 04 2021 12:04:54

%S 13,31,337,701,761,937,983,1151,1279,1831,1933,3191,3803,3851,3911,

%T 7043,7219,7457,7523,7643,9127,9161,9241,9437,9521,9547,9601,9871,

%U 9931,10007,10151,10247,10487,10639,10853,10889,11071,11657,11833,12071,12547,12689

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

%C There are large gaps in this sequence because all terms need to begin with 1, 3, 7, or 9 otherwise the reversal is composite.

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

%o (Python)

%o from sympy import isprime, nextprime

%o def isemirp(p): s = str(p); return s != s[::-1] and isprime(int(s[::-1]))

%o def aupto(limit):

%o   alst, pvec, evec, p = [], [2, 3, 5, 7], [0, 0, 0, 0], 11

%o   while pvec[1] <= limit:

%o     if evec == [0, 1, 1, 0]: alst.append(pvec[1])

%o     pvec = pvec[1:] + [p]; evec = evec[1:] + [isemirp(p)]; p = nextprime(p)

%o   return alst

%o print(aupto(12689)) # _Michael S. Branicky_, Jul 04 2021

%Y Subsequence of A006567 (emirps).

%Y Cf. A003684, A048052, A048054, A071612.

%K nonn,base

%O 1,1

%A _Lars Blomberg_, Jul 01 2021