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A090423 Primes that can be written in binary representation as concatenation of other primes. 8
11, 23, 29, 31, 43, 47, 59, 61, 71, 79, 83, 109, 113, 127, 151, 157, 167, 173, 179, 181, 191, 223, 229, 233, 239, 241, 251, 271, 283, 317, 337, 347, 349, 353, 359, 367, 373, 379, 383, 431, 433, 439, 457, 463, 467, 479, 487, 491, 499, 503, 509, 541, 563, 599, 607 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A090418(a(n)) > 1; subsequence of A090421.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

EXAMPLE

337 is 101010001 in binary,

10 is 2,

10 is 2,

10001 is 17, partition is 10_10_10001, so 337 is in the sequence.

PROG

(Python)

# Primes = [2, ..., 607]

def tryPartioning(binString):   # First digit is not 0

    l = len(binString)

    for t in range(2, l-1):

        substr1 = binString[:t]

        if (int('0b'+substr1, 2) in primes) or (t>=4 and tryPartioning(substr1)):

            substr2 = binString[t:]

            if substr2[0]!='0':

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

                    return 1

    return 0

for p in primes:

    if tryPartioning(bin(p)[2:]):

        print p,

(Haskell)

a090423 n = a090423_list !! (n-1)

a090423_list = filter ((> 1 ) . a090418 . fromInteger) a000040_list

-- Reinhard Zumkeller, Aug 06 2012

CROSSREFS

Cf. A090422, A000040, A004676, A007088.

Sequence in context: A061752 A122259 A157173 * A232085 A086102 A058340

Adjacent sequences:  A090420 A090421 A090422 * A090424 A090425 A090426

KEYWORD

nonn,base

AUTHOR

Reinhard Zumkeller, Nov 30 2003

EXTENSIONS

Corrected by Alex Ratushnyak, Aug 03 2012

STATUS

approved

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Last modified November 26 20:33 EST 2014. Contains 250119 sequences.