A067022 - OEIS

%I #13 Sep 05 2017 07:43:01

%S 0,1,1,2,3,3,4,5,5,6,7,7,8,9,10,11,11,12,13,14,15,15,16,17,18,19,19,

%T 20,21,22,22,23,24,25,26,27,27,28,29,30,31,31,32,33,34,35,35,36,37,38,

%U 39,40,41,41,42,43,44,45,46,47,47,48,49,50,51,51,52,53,54,55,55,56,57,58

%N Exponent of largest power of (n+1)-st prime which is still smaller than the product of first n primes, the n-th primorial.

%H Vincenzo Librandi, <a href="/A067022/b067022.txt">Table of n, a(n) for n = 1..500</a>

%F a(n) = Max{k : p(n+1)^k < A002110(n)}; a(n) < n is trivial.

%e a(1) = floor(log_3(2)) = 0;

%e a(2) = floor(log_5(2*3)) = 1;

%e a(3) = floor(log_7(2*3*5)) = 1;

%e a(4) = floor(log_11(2*3*5*7)) = 2;

%e a(5) = floor(log_13(2*3*5*7*11)) = 3;

%e a(6) = floor(log_17(2*3*5*7*11*13)) = 3;

%e a(7) = floor(log_19(2*3*5*7*11*13*17)) = 4.

%t q[x_] := Apply[Times, Table[Prime[w], {w, 1, x}]];

%t Table[Count[Sign[Table[Prime[w+1]^k-q[w], {k, 1, w}]], -1], {w, 1, 100}]

%Y Cf. A002110, A067021.

%K nonn

%O 1,4

%A _Labos Elemer_, Dec 29 2001

%E Edited by _Jon E. Schoenfield_, Sep 05 2017