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

1,1

Comments

All listed terms are congruent to 1 modulo 12.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

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.

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 *)

Prog

(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
(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

Crossrefs

Cf. A112998, A113000.

Sequence in context: A283527 A190294 A124047 * A004935 A004955 A004975

Adjacent sequences: A113005 A113006 A113007 * A113009 A113010 A113011

Keyword

nonn,easy

Author

Zak Seidov, Jan 03 2006

Extensions

More terms from Robert G. Wilson v, Jan 05 2006

Status

approved