A052034 Primes such that the sum of the squares of their digits is also a prime.

11, 23, 41, 61, 83, 101, 113, 131, 137, 173, 179, 191, 197, 199, 223, 229, 311, 313, 317, 331, 337, 353, 373, 379, 397, 401, 409, 443, 449, 461, 463, 467, 601, 641, 643, 647, 661, 683, 719, 733, 739, 773, 797, 829, 863, 883, 911, 919, 937, 971, 977, 991, 997, 1013

Offset

1,1

Comments

Primes p such that the sum of the squared digits of p is a prime q. For the values of q see A109181.

References

Clifford A. Pickover, A Passion for Mathematics, John Wiley & Sons, Inc., 2005, p. 89.

Charles W. Trigg, Journal of Recreational Mathematics, Vol. 20(2), 1988.

Links

Zak Seidov, Table of n, a(n) for n = 1..10000

Mike Mudge, Morph code, Hands On Numbers Count, Personal Computer World, May 1997, p. 290.

Example

p = 23 is in the sequence because q = 2^2 + 3^2 = 13 is a prime.
9431 -> 9^2 + 4^2 + 3^2 + 1^2 = 107 (which is prime).

Maple

a:=proc(n) local nn, L: nn:=convert(n, base, 10): L:=nops(nn): if isprime(n)= true and isprime(add(nn[j]^2, j=1..L))=true then n else end if end proc: seq(a(n), n=1..1000); # Emeric Deutsch, Jan 08 2008

Mathematica

Select[Prime[Range[250]], PrimeQ[Total[IntegerDigits[#]^2]]&]  (* Harvey P. Dale, Dec 19 2010 *)

Prog

(Python)
from sympy import isprime, primerange
def ok(p): return isprime(sum(int(d)**2 for d in str(p)))
def aupto(limit): return [p for p in primerange(1, limit+1) if ok(p)]
print(aupto(1013)) # Michael S. Branicky, Nov 23 2021

Crossrefs

Cf. A003132, A052035, A091367, A108662, A109181.

Sequence in context: A094376 A086524 A060915 * A077041 A190797 A068842

Adjacent sequences: A052031 A052032 A052033 * A052035 A052036 A052037

Keyword

nonn,base

Author

Patrick De Geest, Dec 15 1999

Extensions

Edited by N. J. A. Sloane, Dec 15 2007 and again on Dec 05 2008 at the suggestion of Zak Seidov

Status

approved