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A051362
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Primes remaining prime if any digit is deleted (zeros allowed).
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14
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23, 37, 53, 73, 113, 131, 137, 173, 179, 197, 311, 317, 431, 617, 719, 1013, 1031, 1097, 1499, 1997, 2239, 2293, 3137, 4019, 4919, 6173, 7019, 7433, 9677, 10193, 10613, 11093, 19973, 23833, 26833, 30011, 37019, 40013, 47933, 73331, 74177
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| These might be called "super-prime numbers". - Jaime Gutierrez (jgutierrez(AT)matematicas.net), Sep 27 2007
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LINKS
| T. D. Noe, Table of n, a(n) for n = 1..100
StackExchange, Deleting any digit yields a prime
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MATHEMATICA
| rpQ[n_]:=Module[{idn=IntegerDigits[n]}, And@@PrimeQ[FromDigits/@ Subsets[IntegerDigits[n], {Length[idn]-1}]]]; Select[Prime[Range[40000]], rpQ]
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PROG
| (Haskell)
import Data.List (inits, tails)
a051362 n = a051362_list !! (n-1)
a051362_list = filter p $ drop 4 a000040_list where
p x = all (== 1) $ map (a010051 . read) $
zipWith (++) (inits $ show x) (tail $ tails $ show x)
-- Reinhard Zumkeller, Dec 17 2011, Aug 24 2011
(PARI) is(n)=my(v=Vec(Str(n)), k); for(i=1, #v, k=eval(concat(vecextract(v, 2^#v-1-2^(i-1)))); if(!isprime(k), return(0))); isprime(n) \\ Charles R Greathouse IV, Oct 05 2011
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CROSSREFS
| Cf. A034302, A010051, A000040.
Sequence in context: A055114 A063643 A057876 * A034302 A057878 A019549
Adjacent sequences: A051359 A051360 A051361 * A051363 A051364 A051365
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KEYWORD
| nonn,base,nice
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AUTHOR
| Harvey P. Dale (hpd1(AT)is2.nyu.edu), May 31 2000
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