A064393 Numbers k such that the exponent of highest power of 2 dividing k! equals the largest prime <= k.

4, 8, 9, 22, 26, 27, 32, 33, 50, 51, 56, 57, 70, 76, 77, 82, 94, 95, 100, 112, 118, 119, 128, 129, 134, 135, 176, 177, 186, 187, 196, 266, 267, 274, 275, 280, 296, 297, 342, 343, 352, 358, 364, 365, 372, 386, 387, 392, 393, 400, 406, 407, 426, 427, 454, 455

Offset

1,1

Comments

[k/2]+[k/4]+[k/8]+[k/16]+... = prevprime(k+1).

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 1001 terms from Harvey P. Dale)

Example

4! = 2^3*3, 8! = 2^7*3^2*5*7, 9! = 2^7*3^4*5*7, 22! = 2^19*3^9*5^4*7^3*11^2*13*17*19.

Maple

for n from 3 to 10^3 do if sum(floor(n/(2^i)), i=1..15) = prevprime(n+1) then printf(`%d, `, n) fi; od:
# second Maple program:
b:= proc(n) option remember;
      `if`(n<1, 0, b(n-1)+padic[ordp](n, 2))
    end:
a:= proc(n) option remember; local k; for k from 1+
      `if`(n=1, 2, a(n-1)) while b(k)<>prevprime(k+1) do od; k
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Jul 10 2022

Mathematica

f[n_] := (t = 0; p = 2; While[s = Floor[n/p]; t = t + s; s > 0, p *= 2]; t); Do[ If[ f[n] == Prime[ PrimePi[n]], Print[n]], {n, 2, 500} ]
lp[n_]:=If[PrimeQ[n], n, NextPrime[n, -1]]; Select[Range[460], IntegerExponent[ #!, 2] == lp[#]&] (* Harvey P. Dale, Mar 02 2014 *)

Crossrefs

Cf. A000040, A011371, A007917, A064394.

Sequence in context: A354869 A378172 A213015 * A372034 A173743 A035326

Adjacent sequences: A064390 A064391 A064392 * A064394 A064395 A064396

Keyword

nonn

Author

Vladeta Jovovic, Sep 29 2001

Extensions

More terms from Robert G. Wilson v and James A. Sellers, Oct 01 2001

Offset changed to 1 by Alois P. Heinz, Jul 10 2022

Status

approved