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A179550 Primes p such that p plus or minus the sum of its digits squared yields a prime in both cases. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A016224 A278173 A142673 * A202662 A202122 A201086

Adjacent sequences:  A179547 A179548 A179549 * A179551 A179552 A179553

KEYWORD

nonn,base

AUTHOR

Carmine Suriano, Jul 19 2010

STATUS

approved

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Last modified July 1 08:17 EDT 2022. Contains 354953 sequences. (Running on oeis4.)