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A335993 High-water marks of the sequence given by the number of twin primes with average n. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Let T(n) be the number of twin primes with average n.  These are the high-water marks of the sequence T(n).

LINKS

Table of n, a(n) for n=1..64.

N. J. A. Sloane, Transforms (The RECORDS transform returns both the high-water marks and the places where they occur).

MATHEMATICA

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 *)

CROSSREFS

The positions at which those high-water marks are attained are given in A335992.

Sequence in context: A029505 A185092 A218337 * A018309 A245481 A039038

Adjacent sequences:  A335990 A335991 A335992 * A335994 A335995 A335996

KEYWORD

nonn

AUTHOR

P. Michael Kielstra, Jul 04 2020

STATUS

approved

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Last modified October 17 07:39 EDT 2021. Contains 348048 sequences. (Running on oeis4.)