A113008 Numbers n such that n, n+1, n+2, n+3 and n+4 are respectively 1,2,3,4,5-almost primes.
15121, 35521, 52321, 117841, 235441, 313561, 398821, 516421, 520021, 531121, 570601, 623641, 761113, 838561, 941041, 1117321, 1190821, 1317361, 1333621, 1336177, 1372081, 1413793, 1424041, 1431361, 1488901, 1513921, 1560121
Offset: 1
Examples
15121 is prime (or 1-almost prime), 15122=2*7561 is semiprime (or 2-almost prime), 15123=3*71*71 is 3-almost prime, 15124=2*2*29*199 is 4-almost prime, 15125=5*5*5*11*11 is 5-almost prime.
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Programs
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Magma
[n: n in PrimesUpTo(2*10^6) | forall{k: k in [1..4] | &+[f[j, 2]: j in [1..#f]] eq k+1 where f is Factorization(n+k)}]; // Vincenzo Librandi, Sep 24 2012 -
Mathematica
f[n_] := Plus @@ Last /@ FactorInteger@n; t = {}; Do[p = Prime[n]; If[Array[ f[p + # ] &, 4] == {2, 3, 4, 5}, AppendTo[t, p]], {n, 126483}]; t (* Robert G. Wilson v *) aprQ[p_]:=Total[FactorInteger[#][[All,2]]]&/@Range[p+1,p+4]=={2,3,4,5}; Select[ Prime[ Range[120000]],aprQ] (* Harvey P. Dale, Dec 17 2022 *) -
PARI
list(lim)=my(v=List(), L=(lim+2)\3, t); forprime(p=3, L\3, forprime(q=3, min(L\p, p), t=3*p*q-2; if(t%12==1 && isprime(t) && isprime((t+1)/2) && bigomega(t+3)==4 && bigomega(t+4)==5, listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Feb 05 2017
Extensions
More terms from Robert G. Wilson v, Jan 05 2006
Comments