A362678 Primes whose digits are prime and in nondecreasing order.

2, 3, 5, 7, 23, 37, 223, 227, 233, 257, 277, 337, 557, 577, 2237, 2333, 2357, 2377, 2557, 2777, 3557, 5557, 22277, 22777, 23333, 23357, 23557, 25577, 33377, 33577, 222337, 222557, 223337, 223577, 233357, 233557, 233777, 235577, 333337, 335557, 355777

Offset: 1

Author

James C. McMahon, Jul 03 2023

Keywords

• nonn
• base

Comments

Intersection of A009994 and A019546.

The subsequence for primes whose digits are prime and in strictly increasing order has just eight terms: 2 3 5 7 23 37 257 2357 (see A177061).

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A009994, A019546, A177061.

Programs

Maple

M:= 7: # for terms with <+ M digits
R:= NULL:
for d from 1 to M do
  S:= NULL:
  for x2 from 0 to d do
    for x3 from 0 to d-x2 do
      for x5 from 0 to d-x2-x3 do
        x7:= d-x2-x3-x5;
        x:= parse(cat(2$x2,3$x3,5$x5,7$x7));
        if isprime(x) then S:= S,x fi;
    od od od;
    R:= R, op(sort([S]));
od:
R;  # Robert Israel, Jul 04 2023

Mathematica

Select[Prime[Range[31000]], AllTrue[d = IntegerDigits[#], PrimeQ] && LessEqual @@ d &] (* Amiram Eldar, Jul 07 2023 *)

PARI

isok(p) = if (isprime(p), my(d=digits(p)); (d == vecsort(d)) && (#select(isprime, d) == #d)); \\ Michel Marcus, Jul 07 2023

Python

from sympy import isprime
from itertools import count, combinations_with_replacement as cwr, islice
def agen(): yield from (filter(isprime, (int("".join(c)) for d in count(1) for c in cwr("2357",d))))
print(list(islice(agen(), 50))) # Michael S. Branicky, Jul 05 2023