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

1,3

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