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 A124057 Numbers n such that n, n+1, n+2 and n+3 are products of exactly 3 primes. 4
 602, 603, 1083, 2012, 2091, 2522, 2523, 2524, 2634, 2763, 3243, 3355, 4202, 4203, 4921, 4922, 4923, 5034, 5035, 5132, 5203, 5282, 5283, 5785, 5882, 5954, 5972, 6092, 6212, 6476, 6962, 6985, 7730, 7731, 7945, 8393, 8825, 8956, 8972, 9188, 9482, 10011 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS n such that n, n+1, n+2 and n+3 are 3-almost primes. Subset of A113789 Numbers n such that n, n+1 and n+2 are products of exactly 3 primes. A067813 has some runs of up to 7 consecutive 3-almost primes (i.e. starting 211673). But there cannot be 8 consecutive 3-almost primes, as every run of 8 consecutive positive integers contains exactly one multiple of 8 = 2^3 and only 8 of all positive multiples of 8 is a 3-almost prime (i.e. all larger multiples have at least 4 prime factors, with multiplicity). A subset of A045940. - Zak Seidov, Nov 05 2006 LINKS D. W. Wilson, Table of n, a(n) for n = 1..10000 FORMULA n, n+1, n+2 and n+3 are all elements of A014612. n and n+1 are elements of A113789. EXAMPLE a(1) = 602 because 602 = 2 * 7 * 43 and 603 = 3^2 * 67 and 604 = 2^2 * 151 and 605 = 5 * 11^2 are all 3-almost primes. a(2) = 603 because 603 = 3^2 * 67 and 604 = 2^2 * 151 and 605 = 5 * 11^2 and 606 = 2 * 3 * 101 are all 3-almost primes. a(3) = 1083 because 1083 = 3 * 19^2 and 1084 = 2^2 * 271 and 1085 = 5 * 7 * 31 and 1086 = 2 * 3 * 181 are all 3-almost primes. a(4) = 2012 because 2012 = 2^2 * 503, 2013 = 3 * 11 * 61, 2014 = 2 * 19 * 53, 2015 = 5 * 13 * 31. a(5) = 2091 because 2091 = 3 * 17 * 41, 2092 = 2^2 * 523, 2093 = 7 * 13 * 23, 2094 = 2 * 3 * 349. MAPLE with(numtheory): a:=proc(n) if bigomega(n)=3 and bigomega(n+1)=3 and bigomega(n+2)=3 and bigomega(n+3)=3 then n else fi end: seq(a(n), n=1..15000); # Emeric Deutsch, Nov 07 2006 MATHEMATICA okQ[{a_, b_, c_, d_}]:=Union[{a, b, c, d}]=={3}; Flatten[Position[Partition[ PrimeOmega[ Range[11000]], 4, 1], _?(okQ)]] (* Harvey P. Dale, Sep 23 2012 *) PROG (PARI) is(n)=if(!isprime((n+3)\4), return(0)); for(k=n, n+3, if(bigomega(k)!=3, return(0))); 1 \\ Charles R Greathouse IV, Feb 05 2017 (PARI) list(lim)=my(v=List(), u=v, t); forprime(p=2, lim\4, forprime(q=2, min(lim\(2*p), p), t=p*q; forprime(r=2, min(lim\t, q), listput(u, t*r)))); u=Set(u); for(i=4, #u, if(u[i]-u[i-3]==3, listput(v, u[i-3]))); Vec(v) \\ Charles R Greathouse IV, Feb 05 2017 CROSSREFS Cf. A000040, A014612, A056809, A067813, A113789, A045940. Sequence in context: A107440 A218055 A045940 * A252435 A363830 A045941 Adjacent sequences: A124054 A124055 A124056 * A124058 A124059 A124060 KEYWORD easy,nonn AUTHOR Jonathan Vos Post, Nov 03 2006 EXTENSIONS More terms from Zak Seidov, Nov 05 2006 More terms from Emeric Deutsch, Nov 07 2006 STATUS approved

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Last modified November 29 07:03 EST 2023. Contains 367429 sequences. (Running on oeis4.)