|
|
A281424
|
|
Numbers k such that 16*(10^k - 1)/3 + 1 is prime.
|
|
0
|
|
|
6, 23, 65, 82, 108, 188, 300, 342, 401, 584, 1570, 4119, 10030, 24870, 34710
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
All prime numbers of the form 16*(10^k - 1)/3 + 1 are terms of A002476.
For any k = a(n), the m-index of 16*(10^k - 1)/3 + 1 in sequence 6m+1 contains exactly a(n) digits, and each digit is 8. E.g., while k = a(1) = 6, 16*(10^6 - 1)/3 + 1 = 6*888888 + 1 = 5333329.
In any number of form 16*(10^k - 1)/3 + 1, its first digit is 5, its two last digits are 29, and each other digit that is between (5...29) is 3.
For k=1, k=2, k=3, the numbers of form 16*(10^k - 1)/3 + 1 are squares of the primes 7, 23, and 73, respectively (see A001248).
Equivalently defined as primes of the form (16*10^k-13)/3. - Tyler Busby, Apr 16 2024
|
|
LINKS
|
|
|
EXAMPLE
|
For k = a(1) = 6, 16*(10^6 - 1)/3 + 1 = 5333329 and 16*(10^6 - 1)/3 + 1 is prime.
|
|
MATHEMATICA
|
|
|
PROG
|
(Python)
from sympy import isprime
def afind(limit, startk=1):
pow10 = 10**startk
for k in range(startk, limit+1):
if isprime(16*(pow10 - 1)//3 + 1): print(k, end=", ")
pow10 *= 10
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,more
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|