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

1,1

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

Links

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

Example

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.

Prog

(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

Crossrefs

Cf. A004022 (repunit primes).

Sequence in context: A088136 A164932 A086244 * A072185 A105898 A247228

Adjacent sequences: A091936 A091937 A091938 * A091940 A091941 A091942

Keyword

base,nonn

Author

Rick L. Shepherd, Feb 16 2004

Status

approved