A179550 Primes p such that p plus or minus the sum of its digits squared yields a prime in both cases.

13, 127, 457, 1429, 1553, 1621, 2273, 2341, 2837, 4129, 4231, 4561, 4813, 5119, 5519, 5531, 6121, 6451, 6547, 8161, 8167, 8219, 8237, 8783, 8819, 8831, 8941, 9511, 10267, 10559, 11299, 11383, 12809, 13183, 15091, 15569, 16573, 17569, 17659, 18133

Offset: 1

Author

Carmine Suriano, Jul 19 2010

Keywords

• nonn
• base

Examples

			a(5)=1553 since 1553+(1^2+5^2+5^2+3^2)=1553+60=1613 is a prime AND 1553-(1^2+5^2+5^2+3^2)=1553-60=1493 is a prime again.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A076162, A076163, A179549.

Programs

Maple

filter:= proc(p) local t,r;
if not isprime(p) then return false fi;
r:= add(t^2, t=convert(p,base,10));
isprime(p+r) and isprime(p-r);
end proc:
select(filter, [seq(i,i=3..20000,2)]); # Robert Israel, Mar 30 2021

Mathematica

Select[Prime[Range[2100]],AllTrue[#+{Total[IntegerDigits[#]^2],-Total[ IntegerDigits[ #]^2]},PrimeQ]&] (* Harvey P. Dale, Aug 07 2021 *)

PARI

sumdd(n) = {digs = digits(n, 10); return (sum(i=1, #digs, digs[i]^2));}
lista(nn) = {forprime(p=2, nn, s = sumdd(p); if (isprime(p+s) && isprime(p-s), print1(p, ", ")););} \\ Michel Marcus, Jul 25 2013

Python

from sympy import isprime, primerange
def sumdd(n): return sum(int(d)**2 for d in str(n))
def list(nn):
  for p in primerange(2, nn+1):
    s = sumdd(p)
    if isprime(p-s) and isprime(p+s): print(p, end=", ")
list(18133) # Michael S. Branicky, Mar 30 2021 after Michel Marcus