A091939 Prime numbers with prime sum of any two digits.

11, 23, 29, 41, 43, 47, 61, 67, 83, 89, 211, 2111, 4111, 11161, 11411, 16111, 111121, 111211, 111611, 112111, 611111, 1111211, 1114111, 11111141, 11111161, 11141111, 61111111, 1111111121, 1111111411, 1111211111, 1111411111, 1121111111

Offset: 1

Author

Rick L. Shepherd, Feb 16 2004

Keywords

• base
• nonn

Comments

All repunit primes (A004022) are terms. All other terms contain exactly one nonzero even digit. All non-repunit terms with k>2 digits must contain exactly k-1 copies of the digit 1, including final digit 1 and the remaining digit must be either 2, 4, or 6.

a(3330) has 1001 digits. - Michael S. Branicky, Dec 13 2023

Examples

			2111 is a term because it is prime and all sums of any two of its digits are 2+1 = 3 or 1+1 = 2, both of which are primes.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..3329

Crossrefs

Cf. A004022 (repunit primes).

Programs

Python

from gmpy2 import is_prime
from itertools import count, islice
def agen(): # generator of terms
    yield from [11, 23, 29, 41, 43, 47, 61, 67, 83, 89]
    for k in count(3):
        b = (10**k-1)//9
        if is_prime(b): yield b
        dlst = [j for j in [1, 3, 5] if (k+j)%3]
        for i in range(1, k):
            c = 10**i
            for d in dlst:
                if is_prime(b + c*d): yield b + c*d
print(list(islice(agen(), 32))) # Michael S. Branicky, Dec 13 2023