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A056815
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Primes with prime "look and say" descriptions.
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11
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3, 7, 17, 23, 113, 127, 137, 193, 199, 223, 233, 271, 311, 313, 331, 359, 367, 373, 431, 433, 439, 463, 479, 499, 503, 523, 587, 607, 641, 677, 691, 733, 757, 773, 797, 809, 821, 823, 829, 853, 919, 997, 1009, 1069, 1123, 1129, 1171, 1181, 1187, 1223, 1277
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OFFSET
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1,1
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COMMENTS
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The "look and say" descriptions of some of these primes are themselves also terms of this sequence (for example, the one for 373). - Alonso del Arte, Mar 01 2012
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REFERENCES
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David Wells, Prime Numbers: The Most Mysterious Figures in Math. Hoboken, New Jersey: John Wiley & Sons (2005): 41.
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LINKS
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FORMULA
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EXAMPLE
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193 is prime and its "look and say" description A045918(193) = 111913, is also prime, so 193 belongs to the sequence.
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MATHEMATICA
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LookAndSayA[ n_] := FromDigits@Flatten@((Through[ {Length, First}[ # ] ] &) /@ Split@IntegerDigits@n); Select[Prime@Range[210], PrimeQ@LookAndSayA@# &] (* Ray Chandler, Jan 12 2007 *)
(* Emmanuel Vantieghem, Jan 26 2012, reports that the above Mma program is incorrect, because the LookAndSayA function can give wrong answers. Here is a better function (b and c to be substituted by suitable numbers): *)
LookAndSayA[n_] := FromDigits@Flatten@(IntegerDigits/@Flatten@
((Through[{Length, First}[#]]&)/@Split@IntegerDigits@n)); W=Select[Prime@Range[b, c], PrimeQ@LookAndSayA@#&]
(* Robert G. Wilson v then commented (Jan 27 2012) that the following version is cleaner: *)
LookAndSayA[n_] := FromDigits@ Flatten@ IntegerDigits@ Flatten[
Through[{Length, First}[#]] & /@ Split@ IntegerDigits@ n]
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PROG
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(Haskell)
a056815 n = a056815_list !! (n-1)
a056815_list = filter ((== 1) . a010051' . a045918) a000040_list
(Python)
from sympy import isprime, sieve
from itertools import groupby, islice
def LS(n): return int(''.join(str(len(list(g)))+k for k, g in groupby(str(n))))
def agen(): yield from (p for p in sieve if isprime(LS(p)))
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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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