A076163 -id:A076163 - cp's OEIS frontend

A179549 Primes p such that p minus the sum of the square of its digits yields a prime.

13, 53, 127, 233, 257, 293, 457, 521, 541, 547, 587, 857, 983, 1151, 1153, 1429, 1481, 1489, 1511, 1553, 1559, 1579, 1621, 1753, 1861, 2099, 2129, 2143, 2239, 2273, 2341, 2347, 2383, 2411, 2417, 2459, 2549, 2657, 2677, 2729, 2741, 2789, 2837, 2897, 2927

Offset: 1

Carmine Suriano, Jul 19 2010

This sequence differs from A076163 which takes the absolute value of the difference.

			a(5)=257 since 257-(2^2+5^2+7^2)=179 is a prime.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A076162, A076163.

ssdQ[n_]:=Module[{c=n-Total[IntegerDigits[n]^2]},Positive[c]&&PrimeQ[c]]; Select[Prime[Range[500]],ssdQ] (* Harvey P. Dale, Dec 26 2018 *)

isok(n) = {if (isprime(n), digs = digits(n, 10); isprime(n - sum(i=1, #digs, digs[i]^2));, 0)} \\ Michel Marcus, Jul 18 2013

A-number typo and signs in the example corrected - R. J. Mathar, Oct 23 2010

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

Original entry on oeis.org

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

Carmine Suriano, Jul 19 2010

			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.

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

Cf. A076162, A076163, A179549.

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

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

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

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

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A179549 Primes p such that p minus the sum of the square of its digits yields a prime.

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