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

1,1

Links

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

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 *)

Prog

(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

Crossrefs

Subsequence of A280382.

Sequence in context: A251623 A341079 A045456 * A115103 A241043 A045457

Adjacent sequences: A115164 A115165 A115166 * A115168 A115169 A115170

Keyword

easy,nonn

Author

Cino Hilliard, Mar 03 2006

Status

approved