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

Author

Alex Ratushnyak, Aug 03 2012

Keywords

• nonn
• base

Comments

Subsequence of A090423.

Examples

			31 is 11111 in binary, 11 is 3 in decimal, 111 is 7, partition exists: 11_111, so 31 is in the sequence.
		

Links

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

Crossrefs

Cf. A090423.

Programs

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=', ')