A384876 Smallest number m such that both m-1 and m+1 are products of at least n (not necessarily distinct) primes.

3, 5, 17, 55, 161, 1457, 2431, 13121, 101249, 153089, 2086399, 7991297, 65071999, 72630271, 2829746177, 2975006719, 68278476799, 75389157377, 159703334911, 1570258288639, 9714181341185, 91845775327231, 551785225781249, 2123044908695551, 4560483868737535, 4560483868737535, 424428773098651649

Offset

1,1

Comments

The sequence is nondecreasing. - David A. Corneth, Jun 13 2025

Links

Table of n, a(n) for n=1..27.

Example

The smallest number surrounded by semiprime numbers is 5 (between 4 and 6).
And 17 lies between 16 = 2^4 and 18 = 2*3^2.

Maple

F:= proc(n) local pq, t, x, y, z, p, i, m;
  uses priqueue;
  initialize(pq);
      insert([-2^n, 2$n], pq);
  y:= -infinity; z:= -infinity;
    do
      t:= extract(pq);
      x:= -t[1];
      if x-y=2 or x-z=2 then return x-1 fi;
      z:= y; y:= x; m:= nops(t);
      if t[-1] = 2 then insert([2*t[1], 2$m], pq) fi;
      p:= nextprime(t[-1]);
      for i from m to 2 by -1 while t[i] = t[-1] do
        insert([t[1]*(p/t[-1])^(m+1-i), op(t[2..i-1]), p$(m+1-i)], pq)
      od;
    od
end proc:
seq(F(i), i=1..20); # Robert Israel, Jun 12 2025

Prog

(PARI) a(n) = my(m=2); while((bigomega(m-1)<n) || (bigomega(m+1)<n), m++); m; \\ Michel Marcus, Jun 13 2025

Crossrefs

Cf. A000040, A001222, A099047, A154704, A176462, A384372.

Sequence in context: A177960 A271659 A357442 * A049540 A097144 A219108

Adjacent sequences: A384873 A384874 A384875 * A384877 A384878 A384879

Keyword

nonn

Author

Sinuhe Perea, Jun 12 2025

Extensions

a(10)-a(13) from Alois P. Heinz, Jun 12 2025

a(14)-a(20) from Robert Israel, Jun 12 2025

More terms from David A. Corneth, Jun 13 2025

Status

approved