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

1,1

Comments

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

Links

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

Example

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

Prog

(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

Crossrefs

Sequence in context: A102833 A136078 A230255 * A264778 A142303 A152929

Adjacent sequences: A167628 A167629 A167630 * A167632 A167633 A167634

Keyword

base,nonn

Author

Claudio Meller, Nov 07 2009

Extensions

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

Status

approved