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URL: https://oeis.org/A214754

⇱ A214754 - OEIS

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A214754
Primes that can be written in binary representation as a concatenation of odd primes.
2
23, 29, 31, 47, 59, 61, 71, 79, 109, 113, 127, 151, 157, 167, 179, 191, 223, 229, 233, 239, 241, 251, 271, 283, 317, 349, 359, 367, 373, 379, 383, 431, 433, 439, 457, 463, 467, 479, 487, 491, 499, 503, 509, 541, 563, 599, 607, 631, 701, 719, 727, 733, 743, 751, 757
OFFSET
1,1
COMMENTS
Subsequence of A090423.
LINKS
EXAMPLE
31 is 11111 in binary, 11 is 3 in decimal, 111 is 7, partition exists: 11_111, so 31 is in the sequence.
PROG
(Python)
# oddPrimes = [3, ... , 757]
def tryPartitioning(binString): # First digit is not 0
if binString=='10':
return 0
l = len(binString)
for t in range(2, l-1):
substr1 = binString[:t]
if (int('0b'+substr1, 2) in oddPrimes) or (t>=4 and tryPartitioning(substr1)):
substr2 = binString[t:]
if substr2[0]!='0':
if (int('0b'+substr2, 2) in oddPrimes) or (l-t>=4 and tryPartitioning(substr2)):
return 1
return 0
for p in oddPrimes:
if tryPartitioning(bin(p)[2:]):
print(p, end=', ')
CROSSREFS
Cf. A090423.
Sequence in context: A240898 A244077 A277206 * A344375 A153631 A382239
KEYWORD
nonn,base
AUTHOR
Alex Ratushnyak, Aug 03 2012
STATUS
approved