cp's OEIS Frontend

A342960 Primes p such that p+A003132(p),(p+A003132(p))+A003132(p+A003132(p)), p-A003132(p), and (p-A003132(p))-A003132(p-A003132(p)) are prime.

%I A342960 #11 Apr 09 2021 09:34:31
%S A342960 38377,70957,106867,278177,278393,380377,432199,435763,526397,1093159,
%T A342960 2025577,2761147,3068119,3656129,3672659,5649079,6863173,7366453,
%U A342960 8083937,9015863,9346507,9497353,14198467,15099901,15467423,15479273,16020607,16437427,17602547,18804173,20020019,20794141,22866121
%N A342960 Primes p such that p+A003132(p),(p+A003132(p))+A003132(p+A003132(p)), p-A003132(p), and (p-A003132(p))-A003132(p-A003132(p)) are prime.
%C A342960 The number of digits of p that are not divisible by 3 is divisible by 3.
%H A342960 Robert Israel, <a href="/A342960/b342960.txt">Table of n, a(n) for n = 1..250</a>
%e A342960 a(3) = 106867 is a term because 106867, 106867+A003132(106867) = 107053, 107053+A003132(107053) = 107137, 106867-A003132(106867) = 106681, and 106681-A003132(106681) = 106543 are all prime.
%p A342960 filter:= proc(n) local t,x,d;
%p A342960   if not isprime(n) then return false fi;
%p A342960   d:= add(t^2, t=convert(n,base,10));
%p A342960   x:= n+d;
%p A342960   if not isprime(x) then return false fi;
%p A342960   if not isprime(x+add(t^2,t=convert(x,base,10))) then return false fi;
%p A342960   x:= n-d;
%p A342960   isprime(x) and isprime(x-add(t^2,t=convert(x,base,10)))
%p A342960 end proc:
%p A342960 select(filter, [seq(i,i=3..3*10^7,2)]);
%Y A342960 Contained in A179549 and A179550.
%Y A342960 Cf. A003132.
%K A342960 nonn,base
%O A342960 1,1
%A A342960 _J. M. Bergot_ and _Robert Israel_, Mar 31 2021