A192203 Numbers k such that k, k+1, and k+2 are each the product of exactly 5 distinct primes.

16467033, 18185869, 21134553, 21374353, 21871365, 22247553, 22412533, 22721585, 24845313, 25118093, 25228929, 25345333, 25596933, 26217245, 27140113, 29218629, 29752345, 30323733, 30563245, 31943065, 32663265, 33367893, 36055045, 38269021, 39738061, 40547065

Offset

1,1

Comments

Numbers k such that k, k+1, and k+2 are all members of A046387. - N. J. A. Sloane, Jul 17 2024

A subsequence of A242608 intersect A016813. - M. F. Hasler, May 19 2014

All terms are congruent to 1 mod 4. - Zak Seidov, Dec 22 2014

Links

Zak Seidov, Table of n, a(n) for n = 1..154

Example

a(1)=16467033 because it is the product of 5 distinct primes (3,11,17,149,197), and so are a(1)+1: 16467034 (2,19,23,83,227), and a(1)+2: 16467035 (5,13,37,41,167).

Mathematica

SequencePosition[Table[If[PrimeNu[n]==PrimeOmega[n]==5, 1, 0], {n, 164*10^5, 406*10^5}], {1, 1, 1}][[;; , 1]]+164*10^5-1 (* Harvey P. Dale, Jul 17 2024 *)

Prog

(PARI) forstep(n=1+10^7, 1e8, 4, for(k=n, n+2, issquarefree(k)||next(2)); for(k=n, n+2, omega(k)==5||next(2)); print1((n)", ")) \\ M. F. Hasler, May 19 2014

Crossrefs

Cf. A046387, A140079. Subsequence of A318964 and of A364266.

Cf. A039833, A066509, A176167.

Sequence in context: A216004 A155949 A355095 * A248204 A365812 A178555

Adjacent sequences: A192200 A192201 A192202 * A192204 A192205 A192206

Keyword

nonn

Author

Gil Broussard, Jun 25 2011

Status

approved