A237201 - OEIS

%I #33 Jul 04 2024 20:18:14

%S 2,9,170,4023,632148,4843161124,1981162639374

%N Smallest integer m such that the n consecutive numbers m, m+1, ..., m+n-1 have n prime factors each, counted with multiplicity; a(n) = 0 if no such number exists.

%t Table[First@Select[Range[10^6],Union[PrimeOmega[(#+Range[n]-1)]]==={n}&,1],{n,5}] (* _Wouter Meeussen_, Feb 09 2014 *)

%t With[{po=PrimeOmega[Range[633000]]},Table[SequencePosition[po,PadRight[{},n,n],1][[1,1]],{n,5}]] (* Requires Mathematica version 10 or later *) (* The program generates the first 5 terms of the sequence. *) (* _Harvey P. Dale_, Jun 15 2021 *)

%o (Python)

%o import sympy

%o from sympy import isprime

%o from sympy import factorint

%o def PrimeFact(x):

%o   n = 9930000

%o   lst = []

%o   while n < 10**10:

%o     if not isprime(n):

%o       count = 0

%o       for i in range(n, n+x):

%o         if sum(factorint(i).values()) == x:

%o           count += 1

%o         else:

%o           n += 1

%o           break

%o       if count == x:

%o         return n

%o     else:

%o       n += 1

%o (PARI) for(n=1, 5, for(k=2^n-1, oo, my(found=1); for(j=1, n, if(bigomega(k+j)!=n, found=0; break)); if(found, print1(k+1,", "); break))) \\ _Hugo Pfoertner_, Oct 21 2020

%Y Cf. A001222.

%K nonn,hard,more

%O 1,1

%A _Derek Orr_, Feb 04 2014

%E a(6) from _Giovanni Resta_, Feb 09 2014

%E a(7) from _Giovanni Resta_, Feb 10 2014