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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.
1
2, 9, 170, 4023, 632148, 4843161124, 1981162639374
OFFSET
1,1
MATHEMATICA
Table[First@Select[Range[10^6], Union[PrimeOmega[(#+Range[n]-1)]]==={n}&, 1], {n, 5}] (* Wouter Meeussen, Feb 09 2014 *)
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 *)
PROG
(Python)
import sympy
from sympy import isprime
from sympy import factorint
def PrimeFact(x):
n = 9930000
lst = []
while n < 10**10:
if not isprime(n):
count = 0
for i in range(n, n+x):
if sum(factorint(i).values()) == x:
count += 1
else:
n += 1
break
if count == x:
return n
else:
n += 1
(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
CROSSREFS
Cf. A001222.
Sequence in context: A336213 A038843 A367526 * A053294 A199695 A349691
KEYWORD
nonn,hard,more
AUTHOR
Derek Orr, Feb 04 2014
EXTENSIONS
a(6) from Giovanni Resta, Feb 09 2014
a(7) from Giovanni Resta, Feb 10 2014
STATUS
approved