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A372082 Primes p such that the 10's complement A089186(p) and the concatenations of p and A089186(p) and of A089186(p) and p are all prime.

%I A372082 #11 Jul 07 2024 21:03:21
%S A372082 3,7,17,29,71,83,281,719,1637,2309,3701,4493,5507,6299,7691,8363,9029,
%T A372082 11003,13163,17117,18371,20807,31181,31793,32693,32843,33617,33893,
%U A372082 34211,34673,37277,38453,49409,50591,61547,62723,65327,65789,66107,66383,67157,67307,68207,68819,79193,81629,82883
%N A372082 Primes p such that the 10's complement A089186(p) and the concatenations of p and A089186(p) and of A089186(p) and p are all prime.
%C A372082 If p is a term and starts with 1 to 8, then its 10's complement A089186(p) is also a term.  This is not the case if p starts with 9, as then A089186(A089186(p)) <> p.  For example, 9029 is a term but its 10's complement 971 is not a term.
%H A372082 Robert Israel, <a href="/A372082/b372082.txt">Table of n, a(n) for n = 1..10000</a>
%e A372082 a(3) = 17 is a term because 17 is a prime, its 10's complement 83 is a prime, and the concatenations 1783 and 8317 are primes.
%p A372082 filter:= proc(n) local d,c;
%p A372082 if not isprime(n) then return false fi;
%p A372082 d:= 10^(1+ilog10(n)); c:= d-n;
%p A372082 isprime(c) and isprime(c*d+n) and isprime(n*10^(1+ilog10(c))+c)
%p A372082 end proc:
%p A372082 select(filter, [seq(i,i=3..10000,2)]);
%Y A372082 Cf. A089186. Subset of A083989.
%K A372082 nonn,base
%O A372082 1,1
%A A372082 _Robert Israel_, Jul 03 2024