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A214754 Primes that can be written in binary representation as a concatenation of odd primes. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Subsequence of A090423.

LINKS

Table of n, a(n) for n=1..55.

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 tryPartioning(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 tryPartioning(substr1)):

            substr2 = binString[t:]

            if substr2[0]!='0':

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

                    return 1

    return 0

for p in oddPrimes:

    if tryPartioning(bin(p)[2:]):

        print p,

CROSSREFS

Cf. A090423.

Sequence in context: A240898 A244077 A277206 * A153631 A082943 A061754

Adjacent sequences:  A214751 A214752 A214753 * A214755 A214756 A214757

KEYWORD

nonn,base

AUTHOR

Alex Ratushnyak, Aug 03 2012

STATUS

approved

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Last modified October 23 17:32 EDT 2019. Contains 328373 sequences. (Running on oeis4.)