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

Author

Patrick De Geest, Dec 15 1999

Keywords

• nonn
• base

Comments

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

Examples

			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).
		

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.

Crossrefs

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

Programs

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 *)

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

Extensions

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