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A368704
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a(n) is the greatest integer k whose arithmetic derivative is equal to the n-th primorial, and 0 if no such k exists.
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5
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0, 9, 221, 11021, 1333349, 225450221, 65155115009, 23520996509141, 12442607161209161, 10464232622576957201, 10056127550296456854221, 13766838616355849433396389, 23142055714094182897602595769, 42789661015360144177667200022669, 94522361182930558488466844910827309, 265513312562851938794103367354849976069
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OFFSET
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1,2
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COMMENTS
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a(n) is the greatest integer k for which A003415(k) = A002110(n), and 0 if no such k exists.
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LINKS
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FORMULA
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For n > 1, a(n) = p*q, where p, q are primes, p+q = A002110(n) and q >= p and q - p is minimal. - David A. Corneth, Jan 17 2024 [This depends on Goldbach's conjecture being valid, at least on primorials, for which there is strong empirical evidence though.] - Antti Karttunen, Jan 19 2024
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EXAMPLE
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a(1) = 0 as there are no number k such that A003415(k) = A002110(1) = 2.
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PROG
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(PARI) a(n) = {if(n==1, return(0)); pr = vecprod(primes(n)); prover2 = pr/2; forprime(p = prover2, oo, if(isprime(pr - p), return(p*(pr-p))))} \\ David A. Corneth, Jan 17 2024
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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