A365852 a(1)= 2. For n > 1, a(n) is the least number k such that k, k - a(n-1) and k + a(n-1) all have n prime divisors counted by multiplicity.

2, 93, 138, 372, 552, 1488, 2208, 5952, 8832, 23808, 35328, 95232, 141312, 380928, 565248, 1523712, 2260992, 6094848, 9043968, 24379392, 36175872, 97517568, 144703488, 390070272, 578813952, 1560281088, 2315255808, 6241124352, 9261023232, 24964497408, 37044092928, 99857989632, 148176371712

Offset

1,1

Links

Table of n, a(n) for n=1..33.

Formula

For n >= 2, a(n) = 2^(n-2) * 3 * (27 + 4 * (-1)^n).

Example

a(3) = 138 because 138 = 2 * 3 * 23, 138 - a(2) = 45 = 3^2 * 5, and 138 + a(2) = 231 = 3 * 7 * 11  all have 3 prime divisors, counted by multiplicity.

Maple

f:= proc(n, a) # first n-almost-prime b>a such that b-a and a+b are n-almost-prime
  uses priqueue;
  local Aprimes, v, M, q, w, b;
  M:= 10^1000;
  initialize(Aprimes);
  insert([-2^n, 0, 2], Aprimes);
  do
    v:= extract(Aprimes);
    if v[2] = n then
      b:= -v[1];
      if numtheory:-bigomega(b+a)=n and numtheory:-bigomega(b-a) = n then return b fi
    else
      insert(v+[0, 1, 0], Aprimes);
      q:= nextprime(v[3]);
      w:= v[1]*(q/v[3])^(n-v[2]);
      if w >= -M then insert([w, v[2], q], Aprimes) fi
    fi
  od
end proc:
R:= 2: a:= 2:
for n from 2 to 50 do
  a:= f(n, a);
  R:= R, a;
od:
R;

Crossrefs

Cf. A001222.

Sequence in context: A226404 A166825 A348852 * A042057 A214542 A137322

Adjacent sequences: A365849 A365850 A365851 * A365853 A365854 A365855

Keyword

nonn

Author

Robert Israel, Sep 21 2023

Status

approved