A328091 Card numbers (not equal to a power of 2) for top card reappearing at the top after three shuffles (Monthly problem 12008).

3, 10, 14, 36, 51, 60, 136, 141, 248, 528, 819, 910, 1008, 2080, 4064, 5041, 8256, 13107, 15420, 16320

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..20.

P. Korus (Proposer), A slow shuffle, Problem 12008, Amer. Math. Monthly, 126 (No. 8, 2019), pp. 756-759.

Maple

isA328091 := proc(n)
    local kl, k, l, m, d ;
    # kl is k+l
    for kl from 0 do
        # 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
        if kl > 2*ilog2(n)+2 then
            return false ;
        end if;
        # kl=l+k, l < k
        for k from floor(kl/2) to kl do
            l := kl-k ;
            if l < k and l >= 0 then
                for m from 0 to k-1 do
                    d := (2^(kl+2)-2^(l+1)+1) / (2^(l+m+3)-2^(m+2)+1) ;
                    if type (d, 'integer') and n = 2^m*d then
                        return true ;
                    end if;
                end do:
            end if:
        end do:
    end do:
end proc:
for n from 2 do
    if isA328091(n) then
        print(n) ;
    end if;
end do: # R. J. Mathar, Feb 06 2025

Crossrefs

Cf. A328092.

Sequence in context: A023866 A024593 A128930 * A048852 A226101 A141463

Adjacent sequences: A328088 A328089 A328090 * A328092 A328093 A328094

Keyword

nonn,more

Author

N. J. A. Sloane, Oct 17 2019

Extensions

Extended to 20 terms by R. J. Mathar, Feb 06 2025

Status

approved