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A335993
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High-water marks of the sequence given by the number of twin primes with average n.
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1
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0, 1, 2, 3, 4, 6, 12, 13, 16, 18, 20, 24, 32, 34, 44, 48, 52, 54, 62, 66, 70, 74, 88, 94, 108, 118, 120, 132, 138, 152, 158, 170, 190, 216, 232, 250, 252, 260, 282, 290, 318, 332, 378, 384, 396, 446, 450, 452, 480, 481, 502, 512, 526, 532, 552, 592, 624, 641, 674, 692, 708, 728, 820, 850
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OFFSET
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1,3
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COMMENTS
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Let T(n) be the number of twin primes with average n. These are the high-water marks of the sequence T(n).
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LINKS
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N. J. A. Sloane, Transforms (The RECORDS transform returns both the high-water marks and the places where they occur).
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MATHEMATICA
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m = 10^4; tp = Select[Range[3, m, 2], PrimeQ[#] && Or @@ PrimeQ[# + {-2, 2}] &]; f[n_] := Module[{k = Length @ IntegerPartitions[n, {2}, tp]}, If[MemberQ[tp, n/2], k - 1, k]]; s = {}; fm = 0; Do[f1 = f[n]; If[f1 > fm, fm = f1; AppendTo[s, f1]], {n, 2, m/2, 2}]; Prepend[s, 0] (* Amiram Eldar, Jul 11 2020 *)
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CROSSREFS
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The positions at which those high-water marks are attained are given in A335992.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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