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

1,1

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.

Links

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

Example

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

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[#]]]] &]

Prog

(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

Crossrefs

Cf. A004186, A007500, A095179, A371654.

Sequence in context: A097312 A095179 A074895 * A298536 A331784 A325162

Adjacent sequences: A371650 A371651 A371652 * A371654 A371655 A371656

Keyword

nonn,base,easy

Author

César Eliud Lozada, Apr 01 2024

Status

approved