A368805 Primes whose digits are prime in both base 9 and base 10.

2, 3, 5, 7, 23, 227, 277, 2777, 5333, 5573, 23537, 23753, 25373, 225527, 25737557, 27775337, 27775357, 35275777, 35277233, 37333757, 227773753, 227775533, 232372577, 233752577, 252777737, 337777277, 25322233723, 25322237323, 25322237357, 25322237723, 25322327753, 25322327777, 25322532523

Offset

1,1

Comments

Subsequence of A019546.

Links

Table of n, a(n) for n=1..33.

Example

2777 is in this sequence because it is prime, all its digits are prime and 2777 in base 9 is 3725, whose digits are all prime.

Mathematica

Select[Range[2.1*10^7], PrimeQ[#]&&AllTrue[IntegerDigits[#], PrimeQ]&&AllTrue[IntegerDigits[#, 9], PrimeQ]&] (* or *)
seq1[dignum_, b_] := Module[{s = {}}, Do[s = Join[s, Select[FromDigits[#, b] & /@ Tuples[{2, 3, 5, 7}, k], PrimeQ]], {k, 1, dignum}]; s]; seq[maxdig9_] := Select[Intersection[seq1[maxdig9, 9], seq1[maxdig9, 10]], # <= 9^maxdig9 &]; seq[11] (* Amiram Eldar, Jan 06 2024 *)

Prog

(Python)
from gmpy2 import digits, is_prime
from itertools import count, islice, product
def bgen():
    yield from [2, 3, 5, 7]
    for d in count(2):
        for f in product("2357", repeat=d-1):
            for last in "37":
                yield int("".join(f)+last)
def agen(): yield from (t for t in bgen() if is_prime(t) and set(digits(t, 9)) <= set("2357"))
print(list(islice(agen(), 33))) # Michael S. Branicky, Jan 07 2024

Crossrefs

Cf. A000040, A019546.

Sequence in context: A343834 A070029 A360497 * A262339 A110094 A088054

Adjacent sequences: A368802 A368803 A368804 * A368806 A368807 A368808

Keyword

nonn,base

Author

James C. McMahon, Jan 06 2024

Status

approved