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