A345408 - OEIS

%I #11 Jun 18 2021 20:43:32

%S 1090,2662,2992,3212,4334,4994,5104,5324,6776,7106,9328,9548,10450,

%T 10670,10780,11110,11330,11440,11660,12122,12452,12892,13222,15004,

%U 16786,17446,17666,29092,29482,31912,36352,44644,44834,45454,46654,46664,47474,47864,49094,49294,49484,49684,49894,50104

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

%C Numbers that are in A345409 in more than one way.

%C Interchanging an emirp and its reversal is not counted as a different way.

%H Robert Israel, <a href="/A345408/b345408.txt">Table of n, a(n) for n = 1..10000</a>

%e 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 revdigs:= proc(n) local L,i; L:= convert(n,base,10); add(L[-i]*10^(i-1),i=1..nops(L)) end proc:

%p isemirp1:= proc(n) local r;

%p if not isprime(n) then return false fi;

%p r:= revdigs(n);

%p r > n and isprime(r)

%p end proc:

%p 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 V:= sort(map(t -> t+revdigs(t),E)):

%p M:= select(t -> V[t+1]=V[t], [$1..nops(V)-1]):

%p sort(convert(convert(V[M],set),list));

%o (Python)

%o from collections import Counter

%o from sympy import isprime, nextprime

%o def epgen(start=1, end=float('inf')): # generates unique emirp/prime pairs

%o     p = nextprime(start-1)

%o     while p <= end:

%o         revp = int(str(p)[::-1])

%o         if p < revp and isprime(revp): yield (p, revp)

%o         p = nextprime(p)

%o def aupto(lim):

%o     c = Counter(sum(ep) for ep in epgen(1, lim) if sum(ep) <= lim)

%o     return sorted(s for s in c if c[s] > 1)

%o print(aupto(50105)) # _Michael S. Branicky_, Jun 18 2021

%Y Cf. A006567, A345409.

%K nonn,base

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Jun 18 2021