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A382199
Primes p such that for each digit of p, 2*p*(digit) + 1 is prime.
4
3, 11, 131, 173, 491, 797, 947, 1931, 3583, 4391, 6173, 7937, 32323, 49919, 64499, 79997, 83383, 149111, 232333, 296269, 366161, 477947, 611333, 616169, 616961, 635563, 667673, 969179, 1111991, 1779779, 2232523, 2662669, 2922229, 3444341, 5333353, 5599999, 6853663, 6919691, 6929929
OFFSET
1,1
LINKS
PROG
(PARI) isok(k) = if (isprime(k), my(d=Set(digits(k))); for (i=1, #d, if (!isprime(2*k*d[i]+1), return(0))); return(1)); \\ Michel Marcus, Mar 18 2025
(Python)
from gmpy2 import is_prime, digits
from itertools import count, product
def ok(n): return is_prime(n) and all(is_prime(2*n*d+1) for d in map(int, set(digits(n))))
def agen(): # generator of terms
yield from (k for d in count(1) for p in product("123456789", repeat=d-1) for e in "1379" if ok(int("".join(p)+e)))
print([k for k in range(10**7) if ok(k)]) # Michael S. Branicky, Nov 02 2025
CROSSREFS
Subsequence of primes of A382179.
Sequence in context: A287429 A274664 A219620 * A201611 A088075 A088076
KEYWORD
nonn,base
AUTHOR
Michel Marcus, Mar 18 2025
STATUS
approved