A098391 -id:A098391

Search: a098391 -id:a098391

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A098388

a(n) = floor(log_2(prime(n))).

+10
5

1, 1, 2, 2, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

COMMENTS

a(n) is the greatest k such that 2^k does not exceed prime(n). - David James Sycamore, Sep 14 2021

LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A000523(A000040(n)); A098391(n) = A000523(a(n)).

a(n) = A035100(n) - 1. - Michel Marcus, Sep 17 2017

MAPLE

map(ilog2, select(isprime, [2, seq(2*i+1, i=1..1000)])); # Robert Israel, Jun 08 2015

MATHEMATICA

Floor[Log[2, Prime[Range[105]]]] (* data *) (* parameter changed by Hartmut F. W. Hoft, Jun 02 2015 *)

PROG

(PARI) a(n) = logint(prime(n), 2); \\ Michel Marcus, Sep 17 2017

CROSSREFS

Cf. A000040, A000523, A023196, A035100, A098391.

KEYWORD

nonn,easy

AUTHOR

Reinhard Zumkeller, Sep 06 2004

STATUS

approved

A098392

Prime(n)-Log2(Log2(prime(n))), where Log2=A000523.

+10
3

2, 3, 4, 6, 10, 12, 15, 17, 21, 27, 29, 35, 39, 41, 45, 51, 57, 59, 65, 69, 71, 77, 81, 87, 95, 99, 101, 105, 107, 111, 125, 129, 135, 137, 147, 149, 155, 161, 165, 171, 177, 179, 189, 191, 195, 197, 209, 221, 225, 227, 231, 237, 239, 249, 254, 260, 266, 268, 274, 278

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

a(n) = A000040(n) - A098391(n).

LINKS

Table of n, a(n) for n=1..60.

EXAMPLE

a(10) = A000040(10) - A098391(10) = 29 - 2 = 27.

CROSSREFS

Cf. A098390, A014689, A098386, A098389.

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Sep 06 2004

STATUS

approved

A098393

Prime(n)+Log2(Log2(prime(n))), where Log2=A000523.

+10
3

2, 3, 6, 8, 12, 14, 19, 21, 25, 31, 33, 39, 43, 45, 49, 55, 61, 63, 69, 73, 75, 81, 85, 91, 99, 103, 105, 109, 111, 115, 129, 133, 139, 141, 151, 153, 159, 165, 169, 175, 181, 183, 193, 195, 199, 201, 213, 225, 229, 231, 235, 241, 243, 253, 260, 266, 272, 274, 280

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

a(n) = A000040(n) + A098391(n).

LINKS

Table of n, a(n) for n=1..59.

EXAMPLE

a(10) = A000040(10) + A098391(10) = 29 + 2 = 31.

MATHEMATICA

#+Floor[Log[2, Floor[Log[2, #]]]]&/@Prime[Range[60]] (* Harvey P. Dale, May 07 2017 *)

CROSSREFS

Cf. A098389, A014688, A098387, A098390.

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Sep 06 2004

STATUS

approved

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