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

1,1

Comments

This sequence has 1843 terms, the last being 927368041.

Links

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

Example

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

Prog

(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

Crossrefs

Subsequence of A029743 (primes with distinct digits).

Sequence in context: A260594 A228940 A045311 * A045312 A129672 A259188

Adjacent sequences: A356193 A356194 A356195 * A356197 A356198 A356199

Keyword

nonn,base,fini,full

Author

Zak Seidov, Oct 31 2022

Status

approved