A214754 Primes that can be written in binary representation as a concatenation of odd primes.

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

David Radcliffe, Table of n, a(n) for n = 1..10000

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

Adjacent sequences: A214751 A214752 A214753 * A214755 A214756 A214757

Keyword

nonn,base

Author

Alex Ratushnyak, Aug 03 2012

Status

approved