A117388 a(n) is the smallest n-digit integer such that, if all numbers formed by inserting the exponentiation symbol between any two digits are added up, the sum is prime.

21, 121, 1226, 14423, 111334, 1186896

Offset: 2

Author

Ray G. Opao, Apr 25 2006

Keywords

• base
• more
• nonn

Comments

No zeros are allowed in the decimal representation of a(n).

Examples

			a(5) = 14423 since 1^4423+14^423+144^23+1442^3 is prime.
		

Crossrefs

Cf. A113762.

Programs

Mathematica

(* first do *) Needs["DiscreteMath`Combinatorica`"] (* then *) f[n_] := Block[{k = (10^n - 1)/9}, While[id = IntegerDigits@k; First@ Union@ id == 0 || !PrimeQ[Plus @@ Table[FromDigits@ Take[id, {1, k}]^FromDigits@ Take[id, {k + 1, n}], {k, n - 1}]], k++ ]; k]; Do[Print[f[n]] // Timing, {n, 2, 7}] (* Robert G. Wilson v, Apr 27 2006 *)

Python

from sympy import isprime
from itertools import product
def a(n):
    for p in product("123456789", repeat=n):
        s = "".join(p)
        if isprime(sum(int(s[:i])**int(s[i:]) for i in range(1, n))):
            return int(s)
print([a(n) for n in range(2, 6)]) # Michael S. Branicky, Jun 27 2022

Extensions

a(6) from Robert G. Wilson v and Farideh Firoozbakht, Apr 27 2006

a(7) from Sean A. Irvine, Dec 15 2009