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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.
2

%I #16 Jun 27 2022 11:25:45

%S 21,121,1226,14423,111334,1186896

%N 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.

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

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

%t (* 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 *)

%o (Python)

%o from sympy import isprime

%o from itertools import product

%o def a(n):

%o for p in product("123456789", repeat=n):

%o s = "".join(p)

%o if isprime(sum(int(s[:i])**int(s[i:]) for i in range(1, n))):

%o return int(s)

%o print([a(n) for n in range(2, 6)]) # _Michael S. Branicky_, Jun 27 2022

%Y Cf. A113762.

%K base,more,nonn

%O 2,1

%A _Ray G. Opao_, Apr 25 2006

%E a(6) from _Robert G. Wilson v_ and _Farideh Firoozbakht_, Apr 27 2006

%E a(7) from _Sean A. Irvine_, Dec 15 2009