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%I #16 Jan 25 2021 19:03:05
%S 1933,3391,32687,78623,104087,109891,112103,120283,123127,135469,
%T 136217,161983,162209,162391,163819,179779,193261,198613,198901,
%U 301211,316819,316891,382021,389161,712631,721321,726487,738349,780401,784627,902261,918361,918613,943837,964531,977971,1002247
%N Emirps p such that p+(sum of digits of p) and reverse(p)+(sum of digits of p) are emirps.
%H Robert Israel, <a href="/A340843/b340843.txt">Table of n, a(n) for n = 1..1000</a>
%e a(3) = 32687 is an emirp because 32687 and 78623 are distinct primes. The sum of digits of 32687 is 26. 32687+26 = 32713 and 78623+26 = 78649 are emirps because 32713 and 31723 are distinct primes, as are 78649 and 94687.
%p revdigs:= proc(n) local L,i;
%p L:= convert(n,base,10);
%p add(10^(i-1)*L[-i],i=1..nops(L))
%p end proc:
%p filter:= proc(n) local r,t,n2,n3;
%p if not isprime(n) then return false fi;
%p r:= revdigs(n);
%p if r = n or not isprime(r) then return false fi;
%p t:= convert(convert(n,base,10),`+`);
%p for n2 in [n+t, r+t] do
%p if not isprime(n2) then return false fi;
%p r:= revdigs(n2);
%p if r = n2 or not isprime(r) then return false fi;
%p od;
%p true
%p end proc:
%p select(filter, [seq(i,i=13..10^6,2)]);
%o (Python)
%o from sympy import isprime
%o def sd(n): return sum(map(int, str(n)))
%o def emirp(n):
%o if not isprime(n): return False
%o revn = int(str(n)[::-1])
%o if n == revn: return False
%o return isprime(revn)
%o def ok(n):
%o if not emirp(n): return False
%o if not emirp(n + sd(n)): return False
%o revn = int(str(n)[::-1])
%o return emirp(revn + sd(revn))
%o def aupto(nn): return [m for m in range(1, nn+1) if ok(m)]
%o print(aupto(920000)) # _Michael S. Branicky_, Jan 24 2021
%Y Cf. A006567. Contained in A340842.
%K nonn,base
%O 1,1
%A _J. M. Bergot_ and _Robert Israel_, Jan 23 2021
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