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

2,1

Comments

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

Links

Table of n, a(n) for n=2..7.

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A113762.

Sequence in context: A179441 A164785 A179956 * A053052 A243882 A002299

Adjacent sequences: A117385 A117386 A117387 * A117389 A117390 A117391

Keyword

base,more,nonn

Author

Ray G. Opao, Apr 25 2006

Extensions

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

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

Status

approved