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

1,1

Links

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

Example

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

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

Prog

(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

Crossrefs

Cf. A117388.

Sequence in context: A034101 A034111 A077687 * A032585 A138822 A104297

Adjacent sequences: A113759 A113760 A113761 * A113763 A113764 A113765

Keyword

base,nonn

Author

Ray G. Opao, Jan 18 2006

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

Status

approved