cp's OEIS Frontend

A091939 Prime numbers with prime sum of any two digits.

%I A091939 #10 Dec 13 2023 10:49:24
%S A091939 11,23,29,41,43,47,61,67,83,89,211,2111,4111,11161,11411,16111,111121,
%T A091939 111211,111611,112111,611111,1111211,1114111,11111141,11111161,
%U A091939 11141111,61111111,1111111121,1111111411,1111211111,1111411111,1121111111
%N A091939 Prime numbers with prime sum of any two digits.
%C A091939 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.
%C A091939 a(3330) has 1001 digits. - _Michael S. Branicky_, Dec 13 2023
%H A091939 Michael S. Branicky, <a href="/A091939/b091939.txt">Table of n, a(n) for n = 1..3329</a>
%e A091939 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.
%o A091939 (Python)
%o A091939 from gmpy2 import is_prime
%o A091939 from itertools import count, islice
%o A091939 def agen(): # generator of terms
%o A091939     yield from [11, 23, 29, 41, 43, 47, 61, 67, 83, 89]
%o A091939     for k in count(3):
%o A091939         b = (10**k-1)//9
%o A091939         if is_prime(b): yield b
%o A091939         dlst = [j for j in [1, 3, 5] if (k+j)%3]
%o A091939         for i in range(1, k):
%o A091939             c = 10**i
%o A091939             for d in dlst:
%o A091939                 if is_prime(b + c*d): yield b + c*d
%o A091939 print(list(islice(agen(), 32))) # _Michael S. Branicky_, Dec 13 2023
%Y A091939 Cf. A004022 (repunit primes).
%K A091939 base,nonn
%O A091939 1,1
%A A091939 _Rick L. Shepherd_, Feb 16 2004