A239237 Numbers n such that n^d_1 + n^d_2 + ... n^d_k is prime where d_i is the i-th digit in the decimal representation of n.

10, 20, 203, 230, 308, 309, 330, 350, 503, 603, 650, 960, 1068, 1110, 1206, 1350, 1404, 1480, 1730, 1802, 1860, 1910, 2032, 2038, 2044, 2054, 2250, 2320, 2502, 3044, 3082, 3402, 3970, 4032, 4046, 4072, 4120, 4340, 4450, 4540, 4650, 4908, 5204, 5310, 5402

Offset

1,1

Comments

The number must contain a 0 in its decimal representation. If not, the number is divisible by n.

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000

Example

20^2 + 20^0 = 401 is prime so 20 is a member of this sequence.
308^3 + 308^0 + 308^8 = 80985213602898040129 is prime so 308 is a member of this sequence.

Maple

q:= n-> isprime(add(n^i, i=convert(n, base, 10))):
select(q, [$1..6000])[];  # Alois P. Heinz, Apr 02 2023

Mathematica

Select[Range[5000], PrimeQ@ Total[#^IntegerDigits[#]] &] (* Giovanni Resta, Mar 13 2014 *)

Prog

(Python)
import sympy
from sympy import isprime
def PowOpp(x):
..if str(x).find('0') > -1:
....num = 0
....for i in str(x):
......num += x**int(i)
....if isprime(num):
......return True
x = 1
while x < 10**4:
..if PowOpp(x):
....print(x)
..x += 1
(Python)
from itertools import count, islice
from sympy import isprime
def A239237_gen(startvalue=1): # generator of terms >= startvalue
    return filter(lambda n:'0' in (s:=str(n)) and isprime(sum(s.count(d)*n**int(d) for d in set(s))), count(max(1, startvalue)))
A239237_list = list(islice(A239237_gen(), 20)) # Chai Wah Wu, Apr 02 2023

Crossrefs

Cf. A239236.

Subsequence of A011540.

Sequence in context: A250107 A038693 A217318 * A018990 A280882 A335802

Adjacent sequences: A239234 A239235 A239236 * A239238 A239239 A239240

Keyword

nonn,base

Author

Derek Orr, Mar 13 2014

Status

approved