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A241758
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Smallest prime in representation 2*A241757(n) by sum of two primes, the adding of which in binary requires only one carry.
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3
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2, 5, 13, 5, 17, 17, 5, 17, 5, 5, 13, 17, 5, 13, 5, 17, 37, 17, 5, 13, 17, 17, 29, 37, 41, 5, 5, 17, 13, 5, 13, 17, 5, 37, 41, 17, 5, 73, 5, 89, 13, 97, 5, 13, 17, 37, 41, 29, 137, 5, 5, 41, 5, 41, 13, 193, 5, 5, 17, 193, 17, 17, 37, 41, 37, 97, 53, 73, 53, 5
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OFFSET
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1,1
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LINKS
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FORMULA
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2||Binomial(2*A241757(n), a(n)). Indeed, from the Kummer theorem (see reference) 2^t||Binomial(n,x) if and only if in adding x and n-x in binary we have exactly t carries. A proof of the Kummer theorem in arbitrary base one can find in [Fraenkel & Kontorovich].
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EXAMPLE
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a(2)=5, since A241757(2)=22=5+17, and in binary in sum of 101+10001 involves only one carry.
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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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EXTENSIONS
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STATUS
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approved
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