A327909 a(n) is the smallest start of a run of n or more integers having a prime factor greater than n.

2, 5, 13, 19, 55, 65, 113, 151, 151, 226, 364, 406, 736, 736, 1057, 1057, 1409, 1409, 2059, 2059, 2313, 2313, 2313, 2313, 2313, 2313, 2313, 6007, 6961, 6961, 10305, 12013, 12013, 12013, 12013, 12013, 12026, 12026, 17501, 17501, 17501, 17501, 20833, 20833

Offset

1,1

Comments

Is a(n) an upper bound on A327265(n)? A327265(n) = a(n) at n = 1, 2, 4, and 9.

Links

Thomas Garrison, Table of n, a(n) for n = 1..369

Example

      |     prime     |
   k  | factorization | gpf(k) | tau(k)
  ----+---------------+--------+-------
  151 |      151      |   151  |   2
  152 |   2^3 * 19    |    19  |   8
  153 |   3^2 * 17    |    17  |   6
  154 |  2 * 7 * 11   |    11  |   8
  155 |    5 * 31     |    31  |   4
  156 | 2^2 * 3 * 13  |    13  |  12
  157 |      157      |   157  |   2
  158 |    2 * 79     |    79  |   4
  159 |    3 * 53     |    53  |   4

Maple

A:= Vector(100): A[1]:= 2: count:= 1:
B:= Vector(100):
for i from 2 while count < 100 do
  p:= max(numtheory:-factorset(i));
  for j from 1 to min(p-1, 100) do
    if B[j] = 0 then B[j]:= i fi
  od;
  for j from p to 100 do
    if B[j] > 0 and B[j] <= i-j and A[j] = 0 then A[j]:= B[j]; count:= count+1; fi
  od;
  if p <= 99 then B[p..100]:= 0 fi;
od:
convert(A, list); # Robert Israel, Jan 23 2023

Prog

(PARI) a(n) = {my(k=1); x=0; while(x<n, if(vecmax(factor(k++)[, 1])>n, x++, x=0)); k-n+1; } \\ Jinyuan Wang, Oct 26 2019

Crossrefs

Cf. A006530 (greatest prime factor of n).

Cf. A309981, A327265.

Sequence in context: A191082 A068374 A068371 * A072899 A099982 A298991

Adjacent sequences: A327906 A327907 A327908 * A327910 A327911 A327912

Keyword

nonn

Author

Jon E. Schoenfield, Oct 06 2019

Status

approved