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

1,1

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A076162, A076163, A179549.

Sequence in context: A360437 A278173 A142673 * A202662 A202122 A201086

Adjacent sequences: A179547 A179548 A179549 * A179551 A179552 A179553

Keyword

nonn,base

Author

Carmine Suriano, Jul 19 2010

Status

approved