A113762 Numbers n with nonzero digits in their decimal representation such that when all numbers formed by inserting the exponentiation symbol between any two digits are added up, the sum is prime.

21, 31, 51, 71, 121, 142, 161, 162, 164, 181, 211, 237, 326, 343, 412, 416, 456, 491, 494, 612, 616, 726, 817, 929, 1226, 1228, 1427, 1513, 1622, 1776, 1824, 1828, 1911, 1915, 1975, 2127, 2188, 3716, 5265, 6276, 6321, 6491, 6852, 7739, 14423, 14487, 15297, 16159

Offset: 1

Author

Ray G. Opao, Jan 18 2006

Keywords

• base
• nonn

Examples

			a(6) = 142 because 1^42+14^2 = 197, which is prime.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..55

Crossrefs

Cf. A117388.

Programs

Mathematica

lst = {}; Do[ If[ Min@ IntegerDigits@n > 0, a=0; p=10; While[(w = Floor[n/p]) > 0, a += w^ Mod[n, p]; p*=10]; If[PrimeQ[a], Print[{n, a}]; AppendTo[lst, n]]], {n, 11, 9999}]; lst

Python

from sympy import isprime
from itertools import count, islice, product
def agen():
    for d in count(2):
        for p in product("123456789", repeat=d):
            s = "".join(p)
            if isprime(sum(int(s[:i])**int(s[i:]) for i in range(1, d))):
                yield int(s)
print(list(islice(agen(), 44))) # Michael S. Branicky, Jun 27 2022

Extensions

More terms from Giovanni Resta, Jan 19 2006

More terms from Robert G. Wilson v, Apr 27 2006

a(47) and beyond from Michael S. Branicky, Jun 27 2022