This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A071354 #14 Jul 02 2025 19:29:44 %S A071354 12,18,25,36,42,45,48,55,80,91,95,98,99,100,108,110,112,125,130,132, %T A071354 135,136,140,143,152,153,155,160,161,162,175,184,187,190,192,198,208, %U A071354 216,224,225,228,232,235,238,240,242,245,247,248,261,266,273,275,279,285,286,289 %N A071354 Floor(2^n/n) is odd. %C A071354 A student asked if the floor of 2^n / n was always even. He had a proof when n is prime. There is a shorter proof if you look at the binomial expansion of (1+1)^p. %C A071354 There are infinitely many numbers in this sequence. (Because if n is even, then 2^n*12-n-2 is even, so 2^(2^n*12-n-2) is 4 (mod 6). Define x so that this is 6*x + 4, then dividing by 3 gives 2*x + (4/3), and the floor is an odd number.) - _Jinyuan Wang_, Oct 13 2018 %t A071354 Select[ Range[300], OddQ[ Floor[2^# / # ]] & ] %o A071354 (PARI) for(n=1,1000,if((-1)^(floor(2^n/n))==-1+isprime(n),print1(n,","))) %o A071354 (Python) %o A071354 from itertools import count, islice %o A071354 from sympy import isprime %o A071354 def A071354_gen(startvalue=1): # generator of terms >= startvalue %o A071354 yield from filter(lambda k:not isprime(k) and (1<<k)//k&1,count(max(startvalue,1))) %o A071354 A071354_list = list(islice(A071354_gen(),20)) # _Chai Wah Wu_, Apr 23 2025 %Y A071354 Cf. A000799, A071941. %K A071354 nonn,easy %O A071354 1,1 %A A071354 _R. K. Guy_, Jun 12 2002 %E A071354 More terms from several correspondents, Jun 12 2002