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

Author

Jonathan Vos Post, Jan 24 2009

Keywords

• base
• easy
• nonn
• tabl

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.

Examples

			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
===================================================================================
		

Crossrefs

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

Programs

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