A358463 a(n) is the first average of a twin prime pair that is the sum of two distinct averages of twin prime pairs in exactly n ways.

4, 18, 72, 180, 240, 462, 420, 1062, 660, 1290, 2142, 2130, 2550, 2340, 3822, 6762, 2310, 3540, 4788, 6300, 6360, 5880, 5280, 6270, 7350, 8010, 5850, 15330, 9240, 10890, 13398, 7590, 28548, 19992, 11970, 22542, 23688, 11550, 19140, 20748, 27060, 18060, 36930, 25170, 40152, 29400, 27690, 25410

Offset

0,1

Comments

a(n) is the first term of A014574 that is the sum of two distinct terms of A014574 in exactly n ways.

Links

Robert Israel, Table of n, a(n) for n = 0..605

Example

a(3) = 180 because 180 is the average of twin primes 179 and 181, is the sum of two such averages in exactly 3 ways: 180 = 30 + 150 = 42 + 138 = 72 + 108, and no smaller average of twin primes works.

Maple

M:= select(t -> isprime(t+1) and isprime(t-1), {seq(i, i=6..10^6, 6)}):V:= Vector(max(M)/6):for i from 2 to nops(M) do
  for j from 1 to i-1 do
    s:= M[i]+M[j];
    if s > 10^6 then break fi;
    if member(s, M) then
       V[s/6]:= V[s/6]+1;
    fi
od od:
A:= Array(0..100): A[0]:= 4:
for m in M do
  v:= V[m/6];
  if v <= 100 and A[v] = 0 then A[v]:= m fi
od:
convert(A, list);

Crossrefs

Cf. A014574.

Sequence in context: A050184 A263582 A034352 * A159715 A027261 A290919

Adjacent sequences: A358460 A358461 A358462 * A358464 A358465 A358466

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Nov 17 2022

Status

approved