A045716 a(n) is the binary order (A029837) of the n-th primorial number, A002110(n).
1, 3, 5, 8, 12, 15, 19, 24, 28, 33, 38, 43, 49, 54, 60, 65, 71, 77, 83, 89, 96, 102, 108, 115, 121, 128, 135, 141, 148, 155, 162, 169, 176, 183, 190, 198, 205, 212, 220, 227, 235, 242, 250, 257, 265, 273, 280, 288, 296, 304, 312, 319, 327, 335, 343, 351, 359
Offset: 1
Keywords
Examples
The sixth primorial number is 2*3*5*7*11*13 = 30030, which is in the interval [16385, 32768] = [2^14 + 1, 2^15], so its binary order is a(6)=15. [corrected by _Jon E. Schoenfield_, May 13 2018]
Links
- Michael De Vlieger, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
Table[Ceiling@ Log2[Times @@ Prime@ Range@ n], {n, 57}] (* Michael De Vlieger, Feb 05 2017 *) -
PARI
a(n)=logint(prod(i=1,n,prime(i))-1,2)+1 \\ Charles R Greathouse IV, Feb 06 2017
Formula
a(n) = A054850(n)+1, n >= 2.
Comments