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A155584 Array, read by antidiagonals, of n-th strobogrammatic number in base k. 1
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

If a binary number is palindromatic, 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 A166278

Adjacent sequences:  A155581 A155582 A155583 * A155585 A155586 A155587

KEYWORD

base,easy,nonn,tabl

AUTHOR

Jonathan Vos Post, Jan 24 2009

STATUS

approved

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Last modified June 25 00:41 EDT 2017. Contains 288708 sequences.