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 A088986 Numbers k such that each of k through k+4 are divisible by exactly two primes. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 10 08:45 EDT 2024. Contains 375786 sequences. (Running on oeis4.)