

A090423


Primes that can be written in binary representation as concatenation of other primes.


8



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
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OFFSET

1,1


COMMENTS

A090418(a(n)) > 1; subsequence of A090421.


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000


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]
def tryPartioning(binString): # First digit is not 0
l = len(binString)
for t in range(2, l1):
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 (lt>=4 and tryPartioning(substr2)):
return 1
return 0
for p in primes:
if tryPartioning(bin(p)[2:]):
print p,
(Haskell)
a090423 n = a090423_list !! (n1)
a090423_list = filter ((> 1 ) . a090418 . fromInteger) a000040_list
 Reinhard Zumkeller, Aug 06 2012


CROSSREFS

Cf. A090422, A000040, A004676, A007088.
Sequence in context: A061752 A122259 A157173 * A232085 A086102 A058340
Adjacent sequences: A090420 A090421 A090422 * A090424 A090425 A090426


KEYWORD

nonn,base


AUTHOR

Reinhard Zumkeller, Nov 30 2003


EXTENSIONS

Corrected by Alex Ratushnyak, Aug 03 2012


STATUS

approved



