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A176356
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Numbers which when seen in a mirror are primes (or 1), using calculator-style 7-segment numerals.
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0
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1, 2, 5, 10, 11, 20, 50, 100, 101, 110, 115, 118, 121, 125, 152, 158, 181, 185, 188, 200, 500, 1000, 1010, 1012, 1018, 1022, 1028, 1051, 1081, 1082, 1085, 1100, 1102, 1105, 1108, 1115, 1118, 1121, 1150, 1180, 1181, 1201, 1202, 1210, 1211, 1225, 1250, 1255, 1282, 1285, 1501, 1502, 1520, 1522
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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We construct mirror images of numbers by placing a mirror parallel to the baseline at an acute angle and looking at them from the top of the sheet they are written on.
This defines the mirror images by fixing digits 0, 1 and 8, exchanging 2 and 5, reversing the order of the digits and ignoring leading zeros that may result.
Only entries of A080228 are admitted, because 3's, 4's, 6's, 7's and 9's do not have calculator style images.
If this combined operation on n generates an entry in A008578, n is in this sequence here.
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REFERENCES
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P. Giannopoulos, The Brainteasers, unpublished.
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LINKS
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Table of n, a(n) for n=1..54.
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EXAMPLE
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110 is in the sequence because the mirror is 011 = 11 and prime.
152 is in the sequence because the mirror is 521 = A000040(98), a prime.
31 is not in the sequence because the 3 cannot be mirrored.
115 is in the sequence because the mirror is 211 = A000040(47), a prime.
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MAPLE
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calcmirr := proc(n)
local L, Lm, i ;
L := convert(n, base, 10) ;
Lm := [] ;
for i from 1 to nops(L) do
if op(i, L) = 2 then
Lm := [5, op(Lm)] ;
elif op(i, L) = 5 then
Lm := [2, op(Lm)] ;
elif op(i, L) in {0, 1, 8} then
Lm := [op(i, L), op(Lm)] ;
else
return 0 ;
end if;
end do:
add(op(i, Lm)*10^(i-1), i=1..nops(Lm)) ;
end proc:
isA176356 := proc(n)
local m;
m := calcmirr(n) ;
isprime(m) or (m = 1) ;
end proc:
for n from 1 to 2001 do
if isA176356(n) then
printf("%d, ", n);
end if;
end do: # R. J. Mathar, Sep 24 2011
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PROG
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(PARI program from Franklin T. Adams-Watters. Produces sequence except for initial 1.)
isa(n)=local(r, d); while(n>0, d=n%10; if(d==2, d=5, if(d==5, d=2, if(d==3||d==4|
|d==6||d==7||d==9, return(0)))); r=r*10+d; n\=10); isprime(r)
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CROSSREFS
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Cf. A080228, A080792, A008578
Sequence in context: A032874 A240032 A187792 * A196168 A018514 A018288
Adjacent sequences: A176353 A176354 A176355 * A176357 A176358 A176359
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KEYWORD
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base,easy,nonn
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AUTHOR
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P. Giannopoulos (pgiannop1(AT)yahoo.com), Apr 15 2010, Apr 22 2010
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EXTENSIONS
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Sequence reconstructed with a consistent interpretation of the definition. - R. J. Mathar, Sep 24 2011
Edited by N. J. A. Sloane, Oct 24 2011
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STATUS
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approved
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