cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

User: Sinuhe Perea

Sinuhe Perea's wiki page.

Sinuhe Perea has authored 3 sequences.

A384372 Numbers m such that both m-1 and m+1 are the product of at least 4 not necessarily distinct primes.

Original entry on oeis.org

55, 89, 127, 151, 161, 197, 199, 209, 233, 249, 251, 271, 295, 305, 307, 329, 341, 343, 349, 351, 377, 379, 391, 415, 449, 461, 463, 485, 487, 489, 491, 511, 521, 545, 551, 559, 569, 571, 593, 631, 649, 665, 685, 687, 689, 701, 703, 713, 727, 737, 739, 749, 751
Offset: 1

Views

Author

Sinuhe Perea, May 27 2025

Keywords

Comments

Numbers m such that bigomega(m-1) >= 4 and bigomega(m+1) >= 4.

Examples

			55 is in the sequence because 55-1 = 2*3^3 and 55+1 = 2^3*7 are both products of at least 4 primes.
71 is not in the sequence because 71-1 = 2*5*7.

Crossrefs

Cf. A001222, A176462.

Programs

  • Maple
    q:= n-> andmap(x-> numtheory[bigomega](x)>3, [n-1, n+1]):
select(q, [$1..991])[];  # Alois P. Heinz, Jun 12 2025
  • PARI
    isok(m) = (m>1) && (bigomega(m-1)>3) && (bigomega(m+1)>3); \\ Michel Marcus, Jun 12 2025
  • Python
    from sympy import primeomega
def ok(n): return n>1 and primeomega(n-1)>3 and primeomega(n+1)>3
print(list(filter(ok, range(520))))

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

Original entry on oeis.org

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

Views

Author

Sinuhe Perea, Jun 12 2025

Keywords

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

A354548 Number of edges in the graph of continuous discrete sections for a trivial bundle in a total space of the fiber bundle of size n.

Original entry on oeis.org

1, 8, 56, 296, 1380, 5952
Offset: 1

Views

Author

Sinuhe Perea, Aug 18 2022

Keywords

Comments

A081113 gives the number of vertices in the graph.

Links

Crossrefs

A081113 corresponds to vertices. For a trivial base we get A016777 and for a trivial fiber A000079. For nontrivial but fixed components see A188861 and A126360.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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