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.

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

Offset

1,1

Links

Table of n, a(n) for n=1..7.

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

Adjacent sequences: A237198 A237199 A237200 * A237202 A237203 A237204

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