A098797 Numbers k (with no zero digits) with property that k raised to the product of its digits plus the sum of its digits is prime.

1, 11, 17, 34, 187, 232, 1132, 3112, 3173, 6127, 11413, 12112, 12331, 13213, 14311, 14731, 22231, 23221, 41911, 43117, 51235, 112435, 122113, 131113, 131335, 138181, 142111, 165811, 192163, 211123, 213121, 214513, 225337, 243331, 313171, 321211, 371221, 435415

Offset

1,2

Links

Table of n, a(n) for n=1..38.

Example

a(4)=34: 34^(3*4)+(3+4) = 2386420683693101063, which is prime.

Mathematica

f[n_] := Block[{d = Sort[IntegerDigits[n]]}, d[[1]] != 0 && PrimeQ[n^(Times @@ d) + Plus @@ d]]; Do[ If[ f[n], Print[n]], {n, 36625}] (* Robert G. Wilson v, Oct 23 2004 *)

Prog

(Python)
from math import prod
from sympy import isprime
from itertools import count, islice, product
def agen(): # generator of terms
    for d in count(1):
        for t in product(range(1, 10), repeat=d):
            k = sum(10**i*ti for i, ti in enumerate(t[::-1]))
            if isprime(k**prod(t) + sum(t)): yield k
print(list(islice(agen(), 9))) # Michael S. Branicky, Dec 06 2022

Crossrefs

Cf. A007953, A007954.

Sequence in context: A339180 A086711 A039514 * A271999 A317453 A339247

Adjacent sequences: A098794 A098795 A098796 * A098798 A098799 A098800

Keyword

nonn,base

Author

Ray G. Opao, Oct 05 2004

Extensions

8 more terms from Robert G. Wilson v, Oct 30 2004

a(16)-a(20) from Donovan Johnson, Mar 14 2010

a(21)-a(27) from Michael S. Branicky, Dec 06 2022

a(28)-a(37) from Michael S. Branicky, Jun 12 2023

a(38)-a(39) from Michael S. Branicky, Jun 25 2023

Status

approved