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A155584
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Array, read by antidiagonals, of n-th strobogrammatic number in base k.
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1
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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
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OFFSET
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1,6
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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
===================================================================================
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MAPLE
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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;
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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