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 A173198 Number of pairs of sexy consecutive primes between (A031924(n))^2 and A031924(n)*A031925(n). 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. LINKS J. S. Cheema, Table of n, a(n) for n = 1..1762 Rick Aster, Prime number sieve SAS prime sieve program Eric Weisstein's World of Mathematics, Sexy Primes. Wikipedia, Sexy Primes EXAMPLE 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. MAPLE 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: A031925 := proc(n) A031924(n)+6 ; 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: seq(A173198(n), n=1..80) ; # R. J. Mathar, Feb 15 2010 CROSSREFS Cf. A023201 Sequence in context: A215511 A280105 A063697 * A111381 A063660 A175220 Adjacent sequences:  A173195 A173196 A173197 * A173199 A173200 A173201 KEYWORD nonn AUTHOR Jaspal Singh Cheema, Feb 12 2010 EXTENSIONS Comments condensed by R. J. Mathar, Feb 15 2010 STATUS approved

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Last modified August 3 20:08 EDT 2020. Contains 336201 sequences. (Running on oeis4.)