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.

2, 3, 5, 13, 17, 19, 23, 29, 31, 37, 41, 43, 59, 61, 67, 73, 79, 83, 89, 103, 107, 137, 157, 167, 173, 193, 239, 241, 251, 257, 263, 269, 281, 283, 359, 389, 397, 401, 419, 421, 457, 461, 463, 467, 487, 523, 601, 613, 617, 619, 641, 643, 683

Offset: 1

Author

Zak Seidov, Oct 31 2022

Keywords

• nonn
• base
• fini
• full

Comments

This sequence has 1843 terms, the last being 927368041.

Examples

			For last term: p = 927368041, q = 927368051, q-p = 10, q+p = 1854736092.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..1843

Crossrefs

Subsequence of A029743 (primes with distinct digits).

Programs

Python

from sympy import isprime, nextprime
from itertools import combinations, permutations
def distinct(n): s = str(n); return len(s) == len(set(s))
def afull():
    for d in range(1, 10):
        s = set()
        for p in permutations("0123456789", d):
            if p[0] == "0": continue
            p = int("".join(p))
            if not isprime(p): continue
            q = nextprime(p)
            if not all(distinct(t) for t in [q, q-p, q+p]): continue
            s.add(p)
        yield from sorted(s)
print(list(afull())) # Michael S. Branicky, Nov 01 2022