A335993 High-water marks of the sequence given by the number of twin primes with average n.

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

Offset: 1

Author

P. Michael Kielstra, Jul 04 2020

Keywords

• nonn

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

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

Crossrefs

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

Programs

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 *)