A317744 Prime numbers which result as a concatenation of a decimal number and its binary representation.

11, 311, 5101, 131101, 2511001, 37100101, 51110011, 59111011, 731001001, 931011101, 971100001, 1191110111, 12910000001, 13110000011, 13710001001, 15310011001, 17310101101, 19311000001, 21311010101, 21511010111, 24711110111, 25511111111, 319100111111

Offset

1,1

Comments

The decimal number plus its Hamming weight A000120 must not be divisible by 3. - M. F. Hasler, Apr 05 2024

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

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
(PARI) nb(n)=fromdigits(concat(n, binary(n)))
A317744_upto(N=666)=[p|n<-[1..N], is/*pseudo*/prime(p=nb(n))] \\ M. F. Hasler, Apr 05 2024

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,changed

Author

Philip Mizzi, Aug 05 2018

Status

approved