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A192864
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Lower flat primes: odd primes p such that p-1 is a squarefree number times a power of two.
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3
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3, 5, 7, 11, 13, 17, 23, 29, 31, 41, 43, 47, 53, 59, 61, 67, 71, 79, 83, 89, 97, 103, 107, 113, 131, 137, 139, 149, 157, 167, 173, 179, 191, 193, 211, 223, 227, 229, 233, 239, 241, 257, 263, 269, 277, 281, 283, 293, 311, 313, 317, 331, 337, 347, 349, 353, 359
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OFFSET
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1,1
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COMMENTS
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Broughan & Qizhi show that this sequence has relative density 2*A in the primes, where A = A005596 is Artin's constant. Consequently, there exists a flat number between x and (1+e)x for every e > 0 and large enough x.
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LINKS
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FORMULA
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a(n) ~ k * n * log(n) with k = 1/(2*A) = 1.3370563...
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MATHEMATICA
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Select[Range[3, 360, 2], PrimeQ[#] && SquareFreeQ[(# - 1)/2^IntegerExponent[# - 1, 2]] &] (* Amiram Eldar, Aug 30 2020 *)
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PROG
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(PARI) is(n)=n%2&&isprime(n)&&issquarefree((n-1)>>valuation(n-1, 2)) \\ corrected by Amiram Eldar, Aug 30 2020
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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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