A097257 Numbers whose set of base 11 digits is {0,A}, where A base 11 = 10 base 10.

0, 10, 110, 120, 1210, 1220, 1320, 1330, 13310, 13320, 13420, 13430, 14520, 14530, 14630, 14640, 146410, 146420, 146520, 146530, 147620, 147630, 147730, 147740, 159720, 159730, 159830, 159840, 160930, 160940, 161040, 161050, 1610510

Offset: 0

Author

Ray Chandler, Aug 03 2004

Keywords

• nonn
• base

Comments

n such that there exists a permutation p_1, ..., p_n of 1, ..., n such that i + p_i is a power of 11 for every i.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A001196, A005823, A097251-A097262.

Programs

Mathematica

f[n_] := FromDigits[ IntegerDigits[n, 2] /. {1 -> 10}, 11]; Array[f, 33, 0] (* or much slower *)
fQ[n_] := Union@ Join[{0, 10}, IntegerDigits[n, 11]] == {0, 10}; Select[ Range[0, 1610519], fQ] (* Robert G. Wilson v, May 12 2012 *)
Join[{0},Union[Flatten[Table[FromDigits[#,11]&/@(Join[{10},#]&/@ Tuples[ {10,0},n]),{n,0,5}]]]] (* Harvey P. Dale, Sep 23 2013 *)

PARI

{for(vv=0,32,
bvv=binary(vv);
texp=0;btb=0;
forstep(i=length(bvv),1,-1,btb=btb+10*bvv[i]*11^texp;texp++);
print1(btb,", ") )} \\ Douglas Latimer, May 12 2012

Formula

a(n) = 10*A033047(n).

a(2n) = 11*a(n), a(2n+1) = a(2n)+10.