A088986 Numbers k such that each of k through k+4 are divisible by exactly two primes.

54, 91, 92, 115, 141, 142, 143, 144, 158, 205, 212, 213, 214, 215, 295, 301, 323, 324, 325, 391, 535, 685, 721, 799, 1135, 1345, 1465, 1535, 1711, 1941, 1981, 2101, 2215, 2302, 2303, 2304, 2425, 2641, 3865, 4411, 5461, 6505, 6625, 6925, 7165, 7231, 7261

Offset

1,1

Comments

Identical with A045933 from first-to 38th terms, but deviates later because A045933 includes start of chains with more than 2 prime-factors.

Contrary to longer chains(6,7,8,..) of omega=2 this sequence seems to be either infinite or very long. See A088963-A088985.

Primes counted without multiplicity. - Harvey P. Dale, Oct 20 2011

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..750 from Harvey P. Dale)

Mathematica

Transpose[Select[Partition[Transpose[Select[Table[{n, PrimeNu[n]}, {n, 10000}], Last[#]==2&]][[1]], 5, 1], Last[#]-First[#]==4&]][[1]] (* Harvey P. Dale, Oct 20 2011 *)

Prog

(Python)
from sympy import primefactors
def ok(n):
    return all(len(primefactors(n + i))==2 for i in range(5))
print([n for n in range(1, 8001) if ok(n)]) # Indranil Ghosh, Jul 17 2017
(PARI) lista(kmax) = {my(q = vector(5)); for(k = 6, kmax, q = concat(vecextract(q, "^1"), omega(k) == 2); if(vecmin(q) == 1, print1(k-4, ", "))); } \\ Amiram Eldar, Jul 11 2024

Crossrefs

Cf. A001221, A045933.

Sequence in context: A290146 A071863 A045933 * A259717 A118150 A039779

Adjacent sequences: A088983 A088984 A088985 * A088987 A088988 A088989

Keyword

nonn

Author

Labos Elemer, Sep 30 2003

Status

approved