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%I #15 Jul 20 2024 17:14:24
%S 1,1,2,2,3,4,4,5,6,6,7,7,8,9,9,10,10,11,12,12,13,13,14,15,15,16,16,17,
%T 17,18,19,19,20,20,21,21,22,23,23,24,24,25,26,26,27,27,28,28,29,30,30,
%U 31,31,32,32,33,33,34,35,35,36,36,37,37,38,39,39,40,40,41,41,42,43,43,44
%N a(n) is the smallest number k such that primorial(k)^2 > primorial(n).
%H Alois P. Heinz, <a href="/A076370/b076370.txt">Table of n, a(n) for n = 0..20000</a>
%e For n = 7, primorial(7) = 2*3*5*7*11*13*17 = 510510;
%e primorial(4)^2 = (2*3*5*7)^2 = 210^2 = 44100 < 510510
%e but
%e primorial(5)^2 = (2*3*5*7*11)^2 = 2310^2 = 5336100 > 510510
%e so a(7) = 5.
%p p:= proc(n) option remember; `if`(n<1, 1, p(n-1)*ithprime(n)) end:
%p a:= proc(n) option remember; local k; for k from
%p `if`(n=0, 0, a(n-1)) while p(k)^2<=p(n) do od; k
%p end:
%p seq(a(n), n=0..74); # _Alois P. Heinz_, Jul 20 2024
%t q[x_] := Apply[Times, Table[Prime[j], {j, 1, x}]] Table[Min[Flatten[Position[Table[Sign [q[j]-q[m]/q[j]], {j, 1, m}], 1]]], {m, 1, 250}]
%Y Cf. A002110.
%K nonn,changed
%O 0,3
%A _Labos Elemer_, Oct 14 2002
%E Edited by _Jon E. Schoenfield_, Jul 20 2024
%E a(0)=1 prepended by _Alois P. Heinz_, Jul 20 2024
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