cp's OEIS Frontend

A237201 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.

%I A237201 #33 Jul 04 2024 20:18:14
%S A237201 2,9,170,4023,632148,4843161124,1981162639374
%N A237201 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 A237201 Table[First@Select[Range[10^6],Union[PrimeOmega[(#+Range[n]-1)]]==={n}&,1],{n,5}] (* _Wouter Meeussen_, Feb 09 2014 *)
%t A237201 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 A237201 (Python)
%o A237201 import sympy
%o A237201 from sympy import isprime
%o A237201 from sympy import factorint
%o A237201 def PrimeFact(x):
%o A237201   n = 9930000
%o A237201   lst = []
%o A237201   while n < 10**10:
%o A237201     if not isprime(n):
%o A237201       count = 0
%o A237201       for i in range(n, n+x):
%o A237201         if sum(factorint(i).values()) == x:
%o A237201           count += 1
%o A237201         else:
%o A237201           n += 1
%o A237201           break
%o A237201       if count == x:
%o A237201         return n
%o A237201     else:
%o A237201       n += 1
%o A237201 (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 A237201 Cf. A001222.
%K A237201 nonn,hard,more
%O A237201 1,1
%A A237201 _Derek Orr_, Feb 04 2014
%E A237201 a(6) from _Giovanni Resta_, Feb 09 2014
%E A237201 a(7) from _Giovanni Resta_, Feb 10 2014