A371653 Numbers k such that the number formed by putting the digits of k in descending order is prime.

2, 3, 5, 7, 11, 13, 14, 16, 17, 31, 34, 35, 37, 38, 41, 43, 53, 61, 71, 73, 79, 83, 97, 112, 113, 118, 119, 121, 124, 125, 128, 131, 133, 134, 136, 142, 143, 145, 146, 149, 152, 154, 157, 163, 164, 166, 167, 175, 176, 179, 181, 182, 188, 191, 194, 197, 199

Offset: 1

Author

César Eliud Lozada, Apr 01 2024

Keywords

• nonn
• base
• easy

Comments

Numbers k such that A004186(k) is prime. - Robert Israel, Apr 01 2024

If N is a term then all numbers with the same digits as N are terms too.

Examples

			142 is a term because its digits in decreasing order form 421 and this is prime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A004186, A007500, A095179, A371654.

Programs

Maple

dd:= proc(n) local L,i;
   L:= sort(convert(n,base,10));
   add(L[i]*10^(i-1),i=1..nops(L))
end proc:
select(isprime @ dd, [$1..1000]); # Robert Israel, Apr 01 2024

Mathematica

Select[Range[500], PrimeQ[FromDigits[ReverseSort[IntegerDigits[#]]]] &]

Python

from sympy import isprime
def ok(n): return isprime(int("".join(sorted(str(n), reverse=True))))
print([k for k in range(200) if ok(k)]) # Michael S. Branicky, Apr 01 2024

Python

from itertools import count, islice, combinations_with_replacement
from sympy import isprime
from sympy.utilities.iterables import multiset_permutations
def A371653_gen(): # generator of terms
    for l in count(1):
        xlist = []
        for p in combinations_with_replacement('987654321',l):
            if isprime(int(''.join(p))):
                xlist.extend(int(''.join(d)) for d in multiset_permutations(p))
        yield from sorted(xlist)
A371653_list = list(islice(A371653_gen(),30)) # Chai Wah Wu, Apr 10 2024