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A356196 Consider pairs of consecutive primes {p,q} such that p, q, q-p and q+p all with distinct digits. Sequence gives lesser primes p.

%I A356196 #52 Nov 14 2022 00:37:39
%S A356196 2,3,5,13,17,19,23,29,31,37,41,43,59,61,67,73,79,83,89,103,107,137,
%T A356196 157,167,173,193,239,241,251,257,263,269,281,283,359,389,397,401,419,
%U A356196 421,457,461,463,467,487,523,601,613,617,619,641,643,683
%N A356196 Consider pairs of consecutive primes {p,q} such that p, q, q-p and q+p all with distinct digits. Sequence gives lesser primes p.
%C A356196 This sequence has 1843 terms, the last being 927368041.
%H A356196 Michael S. Branicky, <a href="/A356196/b356196.txt">Table of n, a(n) for n = 1..1843</a>
%e A356196 For last term: p = 927368041, q = 927368051, q-p = 10, q+p = 1854736092.
%o A356196 (Python)
%o A356196 from sympy import isprime, nextprime
%o A356196 from itertools import combinations, permutations
%o A356196 def distinct(n): s = str(n); return len(s) == len(set(s))
%o A356196 def afull():
%o A356196     for d in range(1, 10):
%o A356196         s = set()
%o A356196         for p in permutations("0123456789", d):
%o A356196             if p[0] == "0": continue
%o A356196             p = int("".join(p))
%o A356196             if not isprime(p): continue
%o A356196             q = nextprime(p)
%o A356196             if not all(distinct(t) for t in [q, q-p, q+p]): continue
%o A356196             s.add(p)
%o A356196         yield from sorted(s)
%o A356196 print(list(afull())) # _Michael S. Branicky_, Nov 01 2022
%Y A356196 Subsequence of A029743 (primes with distinct digits).
%K A356196 nonn,base,fini,full
%O A356196 1,1
%A A356196 _Zak Seidov_, Oct 31 2022