A214754 - OEIS

%I #21 Jun 15 2025 20:55:38

%S 23,29,31,47,59,61,71,79,109,113,127,151,157,167,179,191,223,229,233,

%T 239,241,251,271,283,317,349,359,367,373,379,383,431,433,439,457,463,

%U 467,479,487,491,499,503,509,541,563,599,607,631,701,719,727,733,743,751,757

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

%C Subsequence of A090423.

%H David Radcliffe, <a href="/A214754/b214754.txt">Table of n, a(n) for n = 1..10000</a>

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

%o (Python)

%o # oddPrimes = [3, ... , 757]

%o def tryPartitioning(binString):  # First digit is not 0

%o     if binString=='10':

%o         return 0

%o     l = len(binString)

%o     for t in range(2, l-1):

%o         substr1 = binString[:t]

%o         if (int('0b'+substr1,2) in oddPrimes) or (t>=4 and tryPartitioning(substr1)):

%o             substr2 = binString[t:]

%o             if substr2[0]!='0':

%o                 if (int('0b'+substr2,2) in oddPrimes) or (l-t>=4 and tryPartitioning(substr2)):

%o                     return 1

%o     return 0

%o for p in oddPrimes:

%o     if tryPartitioning(bin(p)[2:]):

%o         print(p, end=', ')

%Y Cf. A090423.

%K nonn,base

%O 1,1

%A _Alex Ratushnyak_, Aug 03 2012