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A256872
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Numbers whose binary expansion is the concatenation of the binary expansion of two prime numbers in at least two ways.
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0
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23, 31, 45, 47, 61, 93, 95, 119, 125, 127, 175, 187, 189, 191, 239, 247, 253, 255, 335, 357, 359, 363, 369, 379, 381, 383, 431, 439, 455, 477, 485, 491, 493, 495, 507, 509, 511, 573, 575, 631, 637, 639, 669, 671
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OFFSET
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1,1
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COMMENTS
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A simplified variant (and subsequence) of A257318 (and A090421) where the concatenation of any number of primes is considered.
The subsequence of numbers which are concatenation of 2 primes in at least 3 ways is (93, 95, 189, 191, 239, 253, 335, 381, 383, 669, ...).
All terms are odd. Indeed, if an even number n > 2 is concatenation of two primes (in binary), then it is of the form 'n' = 'floor(n/4)''2' (where 'x' is x in binary), and there is no other possible decomposition.
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LINKS
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FORMULA
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A090418(a(n)) >= 2. (Necessary but not sufficient condition. This actually characterizes elements of A257318. For example, all terms of A090423 satisfy this but many of them are not terms of this sequence.)
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EXAMPLE
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23 = 10111[2] = (10[2])(111[2]) = (101[2])(11[2]) which is (2)(7) resp. (5)(3).
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PROG
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(PARI) is(n, c=2)={for(i=2, #binary(n)-2, bittest(n, i-1)&&isprime(n>>i)&&isprime(n%2^i)&&!c--&&return(1))}
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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