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A362678 Primes whose digits are prime and in nondecreasing order.

%I A362678 #50 Aug 08 2023 17:50:24
%S A362678 2,3,5,7,23,37,223,227,233,257,277,337,557,577,2237,2333,2357,2377,
%T A362678 2557,2777,3557,5557,22277,22777,23333,23357,23557,25577,33377,33577,
%U A362678 222337,222557,223337,223577,233357,233557,233777,235577,333337,335557,355777
%N A362678 Primes whose digits are prime and in nondecreasing order.
%C A362678 Intersection of A009994 and A019546.
%C A362678 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).
%H A362678 Michael S. Branicky, <a href="/A362678/b362678.txt">Table of n, a(n) for n = 1..10000</a>
%p A362678 M:= 7: # for terms with <+ M digits
%p A362678 R:= NULL:
%p A362678 for d from 1 to M do
%p A362678   S:= NULL:
%p A362678   for x2 from 0 to d do
%p A362678     for x3 from 0 to d-x2 do
%p A362678       for x5 from 0 to d-x2-x3 do
%p A362678         x7:= d-x2-x3-x5;
%p A362678         x:= parse(cat(2$x2,3$x3,5$x5,7$x7));
%p A362678         if isprime(x) then S:= S,x fi;
%p A362678     od od od;
%p A362678     R:= R, op(sort([S]));
%p A362678 od:
%p A362678 R;  # _Robert Israel_, Jul 04 2023
%t A362678 Select[Prime[Range[31000]], AllTrue[d = IntegerDigits[#], PrimeQ] && LessEqual @@ d &] (* _Amiram Eldar_, Jul 07 2023 *)
%o A362678 (Python)
%o A362678 from sympy import isprime
%o A362678 from itertools import count, combinations_with_replacement as cwr, islice
%o A362678 def agen(): yield from (filter(isprime, (int("".join(c)) for d in count(1) for c in cwr("2357",d))))
%o A362678 print(list(islice(agen(), 50))) # _Michael S. Branicky_, Jul 05 2023
%o A362678 (PARI) isok(p) = if (isprime(p), my(d=digits(p)); (d == vecsort(d)) && (#select(isprime, d) == #d)); \\ _Michel Marcus_, Jul 07 2023
%Y A362678 Cf. A009994, A019546, A177061.
%K A362678 nonn,base
%O A362678 1,1
%A A362678 _James C. McMahon_, Jul 03 2023