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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.
2
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
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