cp's OEIS Frontend

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

%I A327909 #30 Jan 24 2023 12:34:12
%S A327909 2,5,13,19,55,65,113,151,151,226,364,406,736,736,1057,1057,1409,1409,
%T A327909 2059,2059,2313,2313,2313,2313,2313,2313,2313,6007,6961,6961,10305,
%U A327909 12013,12013,12013,12013,12013,12026,12026,17501,17501,17501,17501,20833,20833
%N A327909 a(n) is the smallest start of a run of n or more integers having a prime factor greater than n.
%C A327909 Is a(n) an upper bound on A327265(n)? A327265(n) = a(n) at n = 1, 2, 4, and 9.
%H A327909 Thomas Garrison, <a href="/A327909/b327909.txt">Table of n, a(n) for n = 1..369</a>
%e A327909       |     prime     |
%e A327909    k  | factorization | gpf(k) | tau(k)
%e A327909   ----+---------------+--------+-------
%e A327909   151 |      151      |   151  |   2
%e A327909   152 |   2^3 * 19    |    19  |   8
%e A327909   153 |   3^2 * 17    |    17  |   6
%e A327909   154 |  2 * 7 * 11   |    11  |   8
%e A327909   155 |    5 * 31     |    31  |   4
%e A327909   156 | 2^2 * 3 * 13  |    13  |  12
%e A327909   157 |      157      |   157  |   2
%e A327909   158 |    2 * 79     |    79  |   4
%e A327909   159 |    3 * 53     |    53  |   4
%p A327909 A:= Vector(100): A[1]:= 2: count:= 1:
%p A327909 B:= Vector(100):
%p A327909 for i from 2 while count < 100 do
%p A327909   p:= max(numtheory:-factorset(i));
%p A327909   for j from 1 to min(p-1,100) do
%p A327909     if B[j] = 0 then B[j]:= i fi
%p A327909   od;
%p A327909   for j from p to 100 do
%p A327909     if B[j] > 0 and B[j] <= i-j and A[j] = 0 then A[j]:= B[j]; count:= count+1; fi
%p A327909   od;
%p A327909   if p <= 99 then B[p..100]:= 0 fi;
%p A327909 od:
%p A327909 convert(A,list); # _Robert Israel_, Jan 23 2023
%o A327909 (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
%Y A327909 Cf. A006530 (greatest prime factor of n).
%Y A327909 Cf. A309981, A327265.
%K A327909 nonn
%O A327909 1,1
%A A327909 _Jon E. Schoenfield_, Oct 06 2019