A115167 Odd numbers k such that k-1 and k+1 have the same number of prime divisors with multiplicity.

5, 19, 29, 43, 51, 55, 67, 69, 77, 89, 115, 151, 171, 173, 187, 189, 197, 233, 237, 243, 245, 249, 267, 271, 283, 285, 291, 295, 307, 317, 329, 341, 343, 349, 355, 403, 405, 411, 427, 429, 435, 437, 461, 489, 491, 507, 569, 571, 593, 597, 603, 605, 653, 665

Offset: 1

Author

Cino Hilliard, Mar 03 2006

Keywords

• easy
• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A280382.

Programs

Mathematica

s = {}; o1 = 0; Do[o2 = PrimeOmega[n]; If[o1 == o2, AppendTo[s, n-1]]; o1 = o2, {n, 2, 666, 2}]; s (* Amiram Eldar, Sep 23 2019 *)
Select[Mean/@SequencePosition[PrimeOmega[Range[700]],{x_,,x}],OddQ] (* Harvey P. Dale, Jan 11 2024 *)

PARI

g(n) = forstep(x=3, n, 2, p1=bigomega(x-1); p2=bigomega(x+1); if(p1==p2, print1(x",")))

Python

from sympy import primeomega
def aupto(limit):
  prv, nxt, alst = 1, 2, []
  for n in range(3, limit+1, 2):
    if prv == nxt: alst.append(n)
    prv, nxt = nxt, primeomega(n+3)
  return alst
print(aupto(665)) # Michael S. Branicky, May 19 2021