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A007597
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Strobogrammatic primes.
(Formerly M4800)
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15
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11, 101, 181, 619, 16091, 18181, 19861, 61819, 116911, 119611, 160091, 169691, 191161, 196961, 686989, 688889, 1008001, 1068901, 1160911, 1180811, 1190611, 1191611, 1681891, 1690691, 1880881, 1881881, 1898681, 1908061, 1960961, 1990661, 6081809, 6100019, 6108019
(list;
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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Primes which are invariant under a 180-degree rotation.
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
C. W. Trigg, "Strobogrammatic Primes and Prime Rotative Twins", J. Rec. Math., 15 (1983), 281-282.
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LINKS
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MATHEMATICA
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lst = {}; fQ[n_] := Block[{allset = {0, 1, 6, 8, 9}, id = IntegerDigits@n}, Union@ Join[id, allset] == allset && Reverse[id /. {6 -> 9, 9 -> 6}] == id]; Do[ If[ PrimeQ@n && fQ@n, AppendTo[lst, n]], {n, 2000000}]; lst (* Robert G. Wilson v, Feb 27 2007 *)
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PROG
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(Python)
from sympy import isprime
from itertools import count, islice, product
def ud(s): return s[::-1].translate({ord('6'):ord('9'), ord('9'):ord('6')})
def agen():
for d in count(2):
for start in "1689":
for rest in product("01689", repeat=d//2-1):
left = start + "".join(rest)
right = ud(left)
for mid in [[""], ["0", "1", "8"]][d%2]:
t = int(left + mid + right)
if isprime(t):
yield t
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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