A167631 Emirps A006567 with a sum of digits and a number of digits which are both primes.

113, 157, 179, 199, 311, 337, 359, 733, 739, 751, 937, 953, 971, 991, 10039, 10079, 10091, 10253, 10273, 10321, 10343, 10453, 10457, 10459, 10499, 10613, 10639, 10651, 10781, 10853, 10859, 10891, 10909, 11003, 11083, 11159, 11197, 11243

Offset: 1

Author

Claudio Meller, Nov 07 2009

Keywords

• base
• nonn

Comments

Subsequence of A006567 and A028834. - R. J. Mathar, Nov 12 2009

Examples

			113 and 311 are distinct primes, and 3 (number of digits) and 5 (1+1+3) are also primes.
		

Links

• Karl-Heinz Hofmann, Table of n, a(n) for n = 1..10000

Programs

PARI

sod(n)=my(s=0);while(n>9,s+=n%10;n\=10);s+n
R(n)=my(v=eval(Vec(Str(n))),s=0);forstep(i=#v,1,-1,s=10*s+v[i]);s
isA167631(n)=my(r); isprime(#Str(n)) && isprime(sod(n)) && isprime(n) && isprime(r=R(n)) && n!=r \\ Charles R Greathouse IV, Nov 10 2009

Python

from sympy import primerange, isprime
A167631 =[]
for power_of_ten in [2,3,5]: # (7 can be added (12 sec. and 26790 terms), 11 not recommended)
    primes = list(primerange(10**(power_of_ten-1),10**power_of_ten))
    for p in primes:
        if str(p) != (p_rev:=str(p)[::-1]):
            if isprime(int(p_rev)):
                if isprime(sum(list(map(int, p_rev.strip())))): A167631.append(p)
print(A167631) # Karl-Heinz Hofmann, Feb 19 2025

Extensions

Edited by Charles R Greathouse IV and R. J. Mathar, Nov 10 2009