A064394 - OEIS

%I #26 Jul 10 2022 17:31:25

%S 4,5,8,9,22,23,26,27,32,33,50,51,56,57,70,71,76,77,82,83,94,95,100,

%T 101,112,113,118,119,128,129,134,135,176,177,186,187,196,197,266,267,

%U 274,275,280,281,296,297,342,343,352,353,358,359,364,365,372,373,386,387

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

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

%H Alois P. Heinz, <a href="/A064394/b064394.txt">Table of n, a(n) for n = 1..10000</a> (first 1001 terms from Harvey P. Dale)

%F A011371(a(n)) = A151799(a(n)).

%e 8! = 2^7*3^2*5*7, 23! = 2^19*3^9*5^4*7^3*11^2*13*17*19*23.

%p for n from 3 to 10^3 do if sum(floor(n/(2^i)), i=1..15) = prevprime(n) then printf(`%d,`,n) fi; od:

%p # second Maple program:

%p b:= proc(n) option remember;

%p       `if`(n<1, 0, b(n-1)+padic[ordp](n, 2))

%p     end:

%p a:= proc(n) option remember; local k; for k from 1+

%p       `if`(n=1, 2, a(n-1)) while b(k)<>prevprime(k) do od; k

%p     end:

%p seq(a(n), n=1..100);  # _Alois P. Heinz_, Jul 10 2022

%t Select[Range[400],IntegerExponent[#!,2]==NextPrime[#,-1]&] (* _Harvey P. Dale_, Sep 24 2013 *)

%o (Python 3.10+)

%o from itertools import count, islice

%o from sympy import prevprime

%o def A064394_gen(startvalue=3): # generator of terms

%o     return filter(lambda n:n-n.bit_count()==prevprime(n),count(max(startvalue,3)))

%o A064394_list = list(islice(A064394_gen(),30)) # _Chai Wah Wu_, Jul 10 2022

%o (PARI) isok(k) = (k>1) && (valuation(k!,2) == precprime(k-1)); \\ _Michel Marcus_, Jul 10 2022

%Y Cf. A000040, A011371, A064393, A151799.

%K nonn

%O 1,1

%A _Vladeta Jovovic_, Sep 29 2001

%E More terms from _James A. Sellers_, Oct 01 2001

%E Name clarified and offset changed to 1 by _Chai Wah Wu_, Jul 10 2022