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A345408 Numbers that are the sum of an emirp and its reversal in more than one way.

%I A345408 #11 Jun 18 2021 20:43:32
%S A345408 1090,2662,2992,3212,4334,4994,5104,5324,6776,7106,9328,9548,10450,
%T A345408 10670,10780,11110,11330,11440,11660,12122,12452,12892,13222,15004,
%U A345408 16786,17446,17666,29092,29482,31912,36352,44644,44834,45454,46654,46664,47474,47864,49094,49294,49484,49684,49894,50104
%N A345408 Numbers that are the sum of an emirp and its reversal in more than one way.
%C A345408 Numbers that are in A345409 in more than one way.
%C A345408 Interchanging an emirp and its reversal is not counted as a different way.
%H A345408 Robert Israel, <a href="/A345408/b345408.txt">Table of n, a(n) for n = 1..10000</a>
%e A345408 a(3) = 2992 is a member because 2992 = 1091 + 1901 = 1181+1811 where 1091 and 1181 and their reversals 1901 and 1811 are primes.
%p A345408 revdigs:= proc(n) local L,i; L:= convert(n,base,10); add(L[-i]*10^(i-1),i=1..nops(L)) end proc:
%p A345408 isemirp1:= proc(n) local r;
%p A345408 if not isprime(n) then return false fi;
%p A345408 r:= revdigs(n);
%p A345408 r > n and isprime(r)
%p A345408 end proc:
%p A345408 E:= select(isemirp1, [seq(seq(seq(i*10^d+j,j=1..10^d-1,2),i=[1,3,7,9]),d=1..4)]):
%p A345408 V:= sort(map(t -> t+revdigs(t),E)):
%p A345408 M:= select(t -> V[t+1]=V[t], [$1..nops(V)-1]):
%p A345408 sort(convert(convert(V[M],set),list));
%o A345408 (Python)
%o A345408 from collections import Counter
%o A345408 from sympy import isprime, nextprime
%o A345408 def epgen(start=1, end=float('inf')): # generates unique emirp/prime pairs
%o A345408     p = nextprime(start-1)
%o A345408     while p <= end:
%o A345408         revp = int(str(p)[::-1])
%o A345408         if p < revp and isprime(revp): yield (p, revp)
%o A345408         p = nextprime(p)
%o A345408 def aupto(lim):
%o A345408     c = Counter(sum(ep) for ep in epgen(1, lim) if sum(ep) <= lim)
%o A345408     return sorted(s for s in c if c[s] > 1)
%o A345408 print(aupto(50105)) # _Michael S. Branicky_, Jun 18 2021
%Y A345408 Cf. A006567, A345409.
%K A345408 nonn,base
%O A345408 1,1
%A A345408 _J. M. Bergot_ and _Robert Israel_, Jun 18 2021