A340843 Emirps p such that p+(sum of digits of p) and reverse(p)+(sum of digits of p) are emirps.
1933, 3391, 32687, 78623, 104087, 109891, 112103, 120283, 123127, 135469, 136217, 161983, 162209, 162391, 163819, 179779, 193261, 198613, 198901, 301211, 316819, 316891, 382021, 389161, 712631, 721321, 726487, 738349, 780401, 784627, 902261, 918361, 918613, 943837, 964531, 977971, 1002247
Offset: 1
Examples
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.
Links
- Robert Israel, Table of n, a(n) for n = 1..1000
Programs
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Maple
revdigs:= proc(n) local L,i; L:= convert(n,base,10); add(10^(i-1)*L[-i],i=1..nops(L)) end proc: filter:= proc(n) local r,t,n2,n3; if not isprime(n) then return false fi; r:= revdigs(n); if r = n or not isprime(r) then return false fi; t:= convert(convert(n,base,10),`+`); for n2 in [n+t, r+t] do if not isprime(n2) then return false fi; r:= revdigs(n2); if r = n2 or not isprime(r) then return false fi; od; true end proc: select(filter, [seq(i,i=13..10^6,2)]);
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Python
from sympy import isprime def sd(n): return sum(map(int, str(n))) def emirp(n): if not isprime(n): return False revn = int(str(n)[::-1]) if n == revn: return False return isprime(revn) def ok(n): if not emirp(n): return False if not emirp(n + sd(n)): return False revn = int(str(n)[::-1]) return emirp(revn + sd(revn)) def aupto(nn): return [m for m in range(1, nn+1) if ok(m)] print(aupto(920000)) # Michael S. Branicky, Jan 24 2021