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%I #18 Dec 17 2022 15:59:55
%S 15121,35521,52321,117841,235441,313561,398821,516421,520021,531121,
%T 570601,623641,761113,838561,941041,1117321,1190821,1317361,1333621,
%U 1336177,1372081,1413793,1424041,1431361,1488901,1513921,1560121
%N Numbers n such that n, n+1, n+2, n+3 and n+4 are respectively 1,2,3,4,5-almost primes.
%C All listed terms are congruent to 1 modulo 12.
%H Charles R Greathouse IV, <a href="/A113008/b113008.txt">Table of n, a(n) for n = 1..10000</a>
%e 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.
%t 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_ *)
%t 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 *)
%o (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
%o (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
%Y Cf. A112998, A113000.
%K nonn,easy
%O 1,1
%A _Zak Seidov_, Jan 03 2006
%E More terms from _Robert G. Wilson v_, Jan 05 2006
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