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%I #28 Jun 15 2021 17:36:21
%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
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