A328091 - OEIS

%I #8 Feb 06 2025 12:05:09

%S 3,10,14,36,51,60,136,141,248,528,819,910,1008,2080,4064,5041,8256,

%T 13107,15420,16320

%N Card numbers (not equal to a power of 2) for top card reappearing at the top after three shuffles (Monthly problem 12008).

%C Powers of 2 are excluded. If they are included we get A328092.

%H P. Korus (Proposer), <a href="https://www.jstor.org/stable/48661400">A slow shuffle</a>, Problem 12008, Amer. Math. Monthly, 126 (No. 8, 2019), pp. 756-759.

%p isA328091 := proc(n)

%p     local kl,k,l,m,d ;

%p     # kl is k+l

%p     for kl from 0 do

%p         # 2^k<=2n, 2^(k-1)<=n, k-1 <=log2(n), k<=log2(n)+1 and l<k, so k+l<=2*log2(n)+2

%p         if kl > 2*ilog2(n)+2 then

%p             return false ;

%p         end if;

%p         # kl=l+k, l < k

%p         for k from floor(kl/2) to kl do

%p             l := kl-k ;

%p             if l < k and l >= 0 then

%p                 for m from 0 to k-1 do

%p                     d := (2^(kl+2)-2^(l+1)+1) / (2^(l+m+3)-2^(m+2)+1) ;

%p                     if type (d,'integer') and n = 2^m*d then

%p                         return true ;

%p                     end if;

%p                 end do:

%p             end if:

%p         end do:

%p     end do:

%p end proc:

%p for n from 2 do

%p     if isA328091(n) then

%p         print(n) ;

%p     end if;

%p end do: # _R. J. Mathar_, Feb 06 2025

%Y Cf. A328092.

%K nonn,more,changed

%O 1,1

%A _N. J. A. Sloane_, Oct 17 2019

%E Extended to 20 terms by _R. J. Mathar_, Feb 06 2025