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 A090423 Primes that can be written in binary representation as concatenation of other primes. 12
 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] from sympy import sieve primes = list(sieve.primerange(1, 608)) 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, end=', ') (Python) from sympy import isprime, primerange def ok(p): b = bin(p)[2:] for i in range(2, len(b)-1): if isprime(int(b[:i], 2)) and b[i] != '0': if isprime(int(b[i:], 2)) or ok(int(b[i:], 2)): return True return False def aupto(lim): return [p for p in primerange(2, lim+1) if ok(p)] print(aupto(607)) # Michael S. Branicky, May 16 2021 (Haskell) a090423 n = a090423_list !! (n-1) a090423_list = filter ((> 1 ) . a090418 . fromInteger) a000040_list -- Reinhard Zumkeller, Aug 06 2012 (PARI) is_A090423(n)={isprime(n)&&for(i=2, #binary(n)-2, bittest(n, i-1)&&isprime(n%2^i)&&is_A090421(n>>i)&&return(1))} \\ M. F. Hasler, Apr 21 2015 CROSSREFS Cf. A090422, A000040, A004676, A007088. Sequence in context: A122259 A157173 A257318 * 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 March 2 17:35 EST 2024. Contains 370498 sequences. (Running on oeis4.)