login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A090423 Primes that can be written in binary representation as concatenation of other primes. 12
11, 23, 29, 31, 43, 47, 59, 61, 71, 79, 83, 109, 113, 127, 151, 157, 167, 173, 179, 181, 191, 223, 229, 233, 239, 241, 251, 271, 283, 317, 337, 347, 349, 353, 359, 367, 373, 379, 383, 431, 433, 439, 457, 463, 467, 479, 487, 491, 499, 503, 509, 541, 563, 599, 607 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
A090418(a(n)) > 1; subsequence of A090421.
LINKS
EXAMPLE
337 is 101010001 in binary,
10 is 2,
10 is 2,
10001 is 17, partition is 10_10_10001, so 337 is in the sequence.
PROG
(Python)
# Primes = [2, ..., 607]
from sympy import sieve
primes = list(sieve.primerange(1, 608))
def tryPartioning(binString): # First digit is not 0
l = len(binString)
for t in range(2, l-1):
substr1 = binString[:t]
if (int('0b'+substr1, 2) in primes) or (t>=4 and tryPartioning(substr1)):
substr2 = binString[t:]
if substr2[0]!='0':
if (int('0b'+substr2, 2) in primes) or (l-t>=4 and tryPartioning(substr2)):
return 1
return 0
for p in primes:
if tryPartioning(bin(p)[2:]):
print(p, end=', ')
(Python)
from sympy import isprime, primerange
def ok(p):
b = bin(p)[2:]
for i in range(2, len(b)-1):
if isprime(int(b[:i], 2)) and b[i] != '0':
if isprime(int(b[i:], 2)) or ok(int(b[i:], 2)): return True
return False
def aupto(lim): return [p for p in primerange(2, lim+1) if ok(p)]
print(aupto(607)) # Michael S. Branicky, May 16 2021
(Haskell)
a090423 n = a090423_list !! (n-1)
a090423_list = filter ((> 1 ) . a090418 . fromInteger) a000040_list
-- Reinhard Zumkeller, Aug 06 2012
(PARI) is_A090423(n)={isprime(n)&&for(i=2, #binary(n)-2, bittest(n, i-1)&&isprime(n%2^i)&&is_A090421(n>>i)&&return(1))} \\ M. F. Hasler, Apr 21 2015
CROSSREFS
Sequence in context: A122259 A157173 A257318 * A232085 A086102 A058340
KEYWORD
nonn,base
AUTHOR
Reinhard Zumkeller, Nov 30 2003
EXTENSIONS
Corrected by Alex Ratushnyak, Aug 03 2012
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 2 17:35 EST 2024. Contains 370498 sequences. (Running on oeis4.)