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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

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Last modified July 4 23:17 EDT 2022. Contains 355086 sequences. (Running on oeis4.)