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10, 10, 12, 8, 11, 14, 12, 15, 18, 19, 21, 21, 25, 31, 19, 23, 32, 29, 27, 28, 43, 36, 36, 35, 42, 51, 52, 46, 43, 53, 45, 55, 41, 55, 51, 46, 71, 52, 66, 60, 54, 62, 75, 66, 56, 67, 91, 65, 78, 75, 77, 97, 62, 80, 90, 81, 68, 78, 89, 99, 86, 90, 98, 98, 106, 96, 90, 84, 105, 89
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OFFSET
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1,1
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COMMENTS
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If you graph a(n) versus n, a clear pattern emerges.
As you go farther along the n-axis, greater are the number of consecutive sexy primes, on average, within each interval obtained.
If one could prove that there is at least one consecutive sexy prime within each interval, this would imply that consecutive sexy primes are infinite.
I suspect all numbers in the sequence are > 0.
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LINKS
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Eric Weisstein's World of Mathematics, Sexy Primes. [The definition in this webpage is unsatisfactory, because it defines a "sexy prime" as a pair of primes.- N. J. A. Sloane, Mar 07 2021].
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EXAMPLE
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The first sexy prime pair with consecutive primes is (23,29) = A031924(1) and A031925(1). Square the first term, you get 529, then take the product of the two primes, you get 667.
Between these two numbers, namely (529,667), there are ten consecutive sexy primes: (541,547), (557,563), (563,569),
(571,577), (587,593), (593,599), (601,607), (607,613), (647,653), and (653 659).
Hence the very first term of the sequence is 10.
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MAPLE
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isA031924 := proc(p) return (isprime(p) and (nextprime(p)-p) = 6 ); end proc:
A031924 := proc(n) local p; if n = 1 then 23; else p := nextprime(procname(n-1)) ; while not isA031924(p) do p := nextprime(p) ; end do ; return p ; end if ; end proc:
A173198 := proc(n) local ulim, llim, a, i ; llim := A031924(n)^2 ; ulim := A031924(n)*A031925(n) ; a := 0 ; for i from llim to ulim-6 do if isA031924(i) then a := a+1 ; end if; end do ; a ; end proc:
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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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