A074851 Numbers k such that k and k+1 both have exactly 2 distinct prime factors.

14, 20, 21, 33, 34, 35, 38, 39, 44, 45, 50, 51, 54, 55, 56, 57, 62, 68, 74, 75, 76, 85, 86, 87, 91, 92, 93, 94, 95, 98, 99, 111, 115, 116, 117, 118, 122, 123, 133, 134, 135, 141, 142, 143, 144, 145, 146, 147, 152, 158, 159, 160, 161, 171, 175, 176, 177, 183, 184

Offset

1,1

Comments

Subsequence of A006049. - Michel Marcus, May 06 2016

Links

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Formula

a(n) seems to be asymptotic to c*n*log(n)^2 with c=0.13...

{k: A001221(k) = A001221(k+1) = 2}. - R. J. Mathar, Jul 18 2023

Example

20=2^2*5 21=3*7 hence 20 is in the sequence.

Mathematica

Flatten[Position[Partition[Table[If[PrimeNu[n]==2, 1, 0], {n, 200}], 2, 1], {1, 1}]] (* Harvey P. Dale, Mar 12 2015 *)

Prog

(PARI) isok(n) = (omega(n) == 2) && (omega(n+1) == 2); \\ Michel Marcus, May 06 2016
(Magma) [n: n in [2..200] | #PrimeDivisors(n) eq 2 and #PrimeDivisors(n+1) eq 2]; // Vincenzo Librandi, Dec 05 2018
(GAP) Filtered([1..200], n->[Size(Set(Factors(n))), Size(Set(Factors(n+1)))]=[2, 2]); # Muniru A Asiru, Dec 05 2018
(Python)
import sympy
from sympy.ntheory.factor_ import primenu
for n in range(1, 200):
    if primenu(n)==2 and primenu(n+1)==2:
        print(n, end=', '); # Stefano Spezia, Dec 05 2018

Crossrefs

Cf. A006049, A006549, A001221.

Analogous sequences for m distinct prime factors: this sequence (m=2), A140077 (m=3), A140078 (m=4), A140079 (m=5), A273879 (m=6).

Cf. A093548.

Equals A255346 \ A321502.

Sequence in context: A349262 A083247 A255346 * A193672 A087678 A144585

Adjacent sequences: A074848 A074849 A074850 * A074852 A074853 A074854

Keyword

easy,nonn

Author

Benoit Cloitre, Sep 10 2002

Status

approved