|
| |
|
|
A317744
|
|
Prime numbers which result as a concatenation of a decimal number and its binary representation.
|
|
0
|
|
|
|
11, 311, 5101, 131101, 2511001, 37100101, 51110011, 59111011, 731001001, 931011101, 971100001, 1191110111, 12910000001, 13110000011, 13710001001, 15310011001, 17310101101, 19311000001, 21311010101, 21511010111, 24711110111, 25511111111, 319100111111
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
LINKS
|
Table of n, a(n) for n=1..23.
|
|
|
EXAMPLE
|
11 is in the sequence because the binary representation of 1 is 1 and the concatenation of 1 and 1 gives 11, which is prime.
931011101 is in the sequence because it is the concatenation of 93 and 1011101 (the binary representation of 93) and is prime.
|
|
|
MATHEMATICA
|
Select[Table[FromDigits[Join[IntegerDigits[n], IntegerDigits[n, 2]]], {n, 400}], PrimeQ] (* Harvey P. Dale, Jul 15 2020 *)
|
|
|
PROG
|
(Python)
from sympy import isprime
def nbinn(n): return int(str(n)+bin(n)[2:])
def ok(n): return isprime(nbinn(n))
def aprefixupto(p): return [nbinn(k) for k in range(1, p+1, 2) if ok(k)]
print(aprefixupto(319)) # Michael S. Branicky, Dec 27 2020
|
|
|
CROSSREFS
|
Cf. A000040, A030458, A052087, A052088, A052089, A127421, A236551, A287300, A287310.
Sequence in context: A001280 A100445 A193890 * A185071 A060495 A251589
Adjacent sequences: A317741 A317742 A317743 * A317745 A317746 A317747
|
|
|
KEYWORD
|
nonn,base,less
|
|
|
AUTHOR
|
Philip Mizzi, Aug 05 2018
|
|
|
STATUS
|
approved
|
| |
|
|
