A067022 Exponent of largest power of (n+1)-st prime which is still smaller than the product of first n primes, the n-th primorial.

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, 20, 21, 22, 22, 23, 24, 25, 26, 27, 27, 28, 29, 30, 31, 31, 32, 33, 34, 35, 35, 36, 37, 38, 39, 40, 41, 41, 42, 43, 44, 45, 46, 47, 47, 48, 49, 50, 51, 51, 52, 53, 54, 55, 55, 56, 57, 58

Offset

1,4

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..500

Formula

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

Example

a(1) = floor(log_3(2)) = 0;
a(2) = floor(log_5(2*3)) = 1;
a(3) = floor(log_7(2*3*5)) = 1;
a(4) = floor(log_11(2*3*5*7)) = 2;
a(5) = floor(log_13(2*3*5*7*11)) = 3;
a(6) = floor(log_17(2*3*5*7*11*13)) = 3;
a(7) = floor(log_19(2*3*5*7*11*13*17)) = 4.

Mathematica

q[x_] := Apply[Times, Table[Prime[w], {w, 1, x}]];
Table[Count[Sign[Table[Prime[w+1]^k-q[w], {k, 1, w}]], -1], {w, 1, 100}]

Crossrefs

Cf. A002110, A067021.

Sequence in context: A210435 A181534 A258703 * A113818 A136746 A003003

Adjacent sequences: A067019 A067020 A067021 * A067023 A067024 A067025

Keyword

nonn

Author

Labos Elemer, Dec 29 2001

Extensions

Edited by Jon E. Schoenfield, Sep 05 2017

Status

approved