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

Author

Sinuhe Perea, Jun 12 2025

Keywords

• nonn

Comments

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

Examples

			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.
		

Crossrefs

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

Programs

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

PARI

a(n) = my(m=2); while((bigomega(m-1)Michel Marcus, Jun 13 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