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.

38377, 70957, 106867, 278177, 278393, 380377, 432199, 435763, 526397, 1093159, 2025577, 2761147, 3068119, 3656129, 3672659, 5649079, 6863173, 7366453, 8083937, 9015863, 9346507, 9497353, 14198467, 15099901, 15467423, 15479273, 16020607, 16437427, 17602547, 18804173, 20020019, 20794141, 22866121

Offset: 1

Author

J. M. Bergot and Robert Israel, Mar 31 2021

Keywords

• nonn
• base

Comments

The number of digits of p that are not divisible by 3 is divisible by 3.

Examples

			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.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..250

Crossrefs

Contained in A179549 and A179550.

Cf. A003132.

Programs

Maple

filter:= proc(n) local t,x,d;
  if not isprime(n) then return false fi;
  d:= add(t^2, t=convert(n,base,10));
  x:= n+d;
  if not isprime(x) then return false fi;
  if not isprime(x+add(t^2,t=convert(x,base,10))) then return false fi;
  x:= n-d;
  isprime(x) and isprime(x-add(t^2,t=convert(x,base,10)))
end proc:
select(filter, [seq(i,i=3..3*10^7,2)]);