A155584 Array, read by antidiagonals, of n-th strobogrammatic number in base k.

0, 0, 1, 0, 1, 2, 0, 1, 3, 3, 0, 1, 4, 5, 4, 0, 1, 5, 10, 7, 5, 0, 1, 6, 17, 13, 9, 6, 0, 1, 7, 26, 21, 28, 15, 7, 0, 1, 8, 37, 31, 65, 40, 17, 8, 0, 1, 9, 50, 43, 126, 85, 82, 21, 9, 0, 1, 8, 65, 57, 217, 156, 257, 91, 27, 10, 0, 1, 8, 10, 73, 344, 259, 626, 273, 112, 31, 11, 0, 1, 8, 11, 80, 513, 400, 1297, 651, 325, 121, 33, 12

Offset

1,6

Comments

If a binary number is palindromic, it is also strobogrammatic. In bases 3 through 7, this is not true, where only digits 0 and 1 can be used, because 8 is not a digit, nor are either of the inversion paid (6,9). I do not show bases beyond 10, although admittedly some letters as digits are other letters upside-down.

Links

Table of n, a(n) for n=1..91.

Example

A[2,4] = 5 because 4th strobogrammatic number base 2 = 101 = 5 (base 10). A[9,8] = 154 because 8th strobogrammatic number base 9 = 181 = 154 (base 10). The array begins: ===================================================================================
..n.|.1.|.2.|.3.|..4.|..5.|...6.|...7.|....8.|....9.|...10.|...11.|....12.|
===================================================================================
k=1.|.0.|.1.|.2.|..3.|..4.|...5.|...6.|....7.|....8.|....9.|...10.|....11.|
k=2.|.0.|.1.|.3.|..5.|..7.|...9.|..15.|...17.|...21.|...27.|...31.|....33.|A006995
k=3.|.0.|.1.|.4.|.10.|.13.|..28.|..40.|...82.|...91.|..112.|..121.|...244.|
k=4.|.0.|.1.|.5.|.17.|.21.|..65.|..85.|..257.|..273.|..325.|..341.|..1025.|
k=5.|.0.|.1.|.6.|.26.|.31.|.126.|.156.|..626.|..651.|..756.|..781.|..3126.|
k=6.|.0.|.1.|.7.|.37.|.43.|.217.|.259.|.1297.|.1333.|.1519.|.1555.|..7777.|
k=7.|.0.|.1.|.8.|.50.|.57.|.344.|.400.|.2402.|.2451.|.2752.|.2801.|.16808.|
k=8.|.0.|.1.|.9.|.65.|.73.|.513.|.585.|.4097.|.4161.|.4617.|.4681.|.32769.|
k=9.|.0.|.1.|.8.|.10.|.80.|..82.|..91.|..154.|..656.|..665.|..728.|...730.|
k=10|.0.|.1.|.8.|.11.|.69.|..88.|..96.|..101.|..111.|..181.|..609.|...619.|A000787
===================================================================================

Maple

strobo := proc(b, n)
        option remember;
        local a;
        if n <=2 then
                return n-1 ;
        elif b = 1 then
                return n-1 ;
        else
                for a from procname(b, n-1)+1 do
                        isstrobo := true ;
                        dgsa := convert(a, base, b) ;
                        for d from 1 to nops(dgsa) do
                                if op(d, dgsa)=1 and op(-d, dgsa) <> 1 then
                                        isstrobo := false;
                                elif op(d, dgsa)=8 and op(-d, dgsa) <> 8 then
                                        isstrobo := false;
                                elif op(d, dgsa)=6 and op(-d, dgsa) <> 9 then
                                        isstrobo := false;
                                elif op(d, dgsa)=9 and op(-d, dgsa) <> 6 then
                                        isstrobo := false;
                                elif op(d, dgsa)=0 and op(-d, dgsa) <> 0 then
                                        isstrobo := false;
                                elif op(d, dgsa) in { 2, 3, 4, 5, 7} then
                                        isstrobo := false;
                                end if;
                        end do;
                        if isstrobo then
                                return a;
                        end if;
                end do:
        end if;
end proc: # R. J. Mathar, Sep 30 2011

Crossrefs

Cf. A006995, A000787, A006072, A068188, A007597.

Sequence in context: A267724 A179329 A089112 * A139600 A198321 A325003

Adjacent sequences: A155581 A155582 A155583 * A155585 A155586 A155587

Keyword

base,easy,nonn,tabl

Author

Jonathan Vos Post, Jan 24 2009

Status

approved