A201147 -id:A201147 - cp's OEIS frontend

A369185 Numbers k such that Omega(k) = 1 + Omega(k+1) = 2 + Omega(k+2).

45, 104, 105, 165, 260, 261, 344, 345, 357, 440, 465, 476, 477, 561, 776, 860, 861, 884, 885, 981, 1016, 1017, 1112, 1160, 1185, 1269, 1281, 1395, 1424, 1544, 1572, 1624, 1644, 1652, 1683, 1808, 1812, 1827, 1905, 1917, 1989, 2037, 2060, 2061, 2097, 2145, 2277, 2444, 2445, 2805, 2817, 2852, 2877

Offset: 1

Zak Seidov and Robert Israel, Jan 15 2024

nonn

Numbers k such that both k and k+1 are in A369139.

			a(4) = 165 is a term because 165 = 3 * 5 * 11 has 3 prime factors (counted with multiplicity), 166 = 2 * 83 has 2 and 167 (which is prime) has 1.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A001222, A369139. Includes x-2 for x in A201147.

N:= 10^4: # for terms <= N
V:= map(numtheory:-bigomega, [$1..N+2]):
select(t -> V[t] = 1 + V[t+1] and V[t] = 2 + V[t+2], [$1..N]);

A201220 Numbers m such that m, m-1, m-2 and m-3 are 1,2,3,4-almost primes respectively.

Original entry on oeis.org

107, 263, 347, 479, 863, 887, 1019, 2063, 2447, 3023, 3167, 3623, 5387, 5399, 5879, 6599, 6983, 7079, 8423, 8699, 9743, 9887, 10463, 11807, 12263, 12347, 14207, 15383, 15767, 18959, 20663, 22343, 23039, 23567, 24239, 27239, 32183, 33647, 33767, 37799

Offset: 1

Antonio Roldán, Nov 28 2011

nonn

Following a suggestion of Claudio Meller.

m is of the form 12k-1, so m-2 is a multiple of 3 and m-3 is a multiple of 4.

			6599 is prime, 6598=2*3299 is semiprime, 6597=3*3*733 is 3-almost prime, 6596=2*2*17*97 is 4-almost prime.

Vincenzo Librandi, Table of n, a(n) for n = 1..1700

Subsequence of A005385 and of A201147.

Cf. A005383, A112998, A113000, A113008, A072875, A093552.

primeCount[n_] := Plus @@ Transpose[FactorInteger[n]][[2]]; Select[Range[40000], primeCount[#] == 1 && primeCount[#-1] == 2 && primeCount[#-2] == 3 && primeCount[#-3] == 4 &] (* T. D. Noe, Nov 28 2011 *)
Select[Range[40000],PrimeOmega[Range[#,#+3]]=={4,3,2,1}&]+3 (* Harvey P. Dale, Dec 10 2011 *)
SequencePosition[PrimeOmega[Range[40000]],{4,3,2,1}][[;;,2]] (* Harvey P. Dale, Oct 08 2023 *)

list(lim)=my(v=List(), L=(lim-2)\3, t); forprime(p=3, L\3, forprime(q=3, min(p, L\p), t=3*p*q+2; if(isprime(t) && isprime((t-1)/2) && bigomega(t-3)==4, listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Feb 02 2017

cp's OEIS Frontend

A369185 Numbers k such that Omega(k) = 1 + Omega(k+1) = 2 + Omega(k+2).

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