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A056815 Primes with prime "look and say" descriptions. 11

%I

%S 3,7,17,23,113,127,137,193,199,223,233,271,311,313,331,359,367,373,

%T 431,433,439,463,479,499,503,523,587,607,641,677,691,733,757,773,797,

%U 809,821,823,829,853,919,997,1009,1069,1123,1129,1171,1181,1187,1223,1277

%N Primes with prime "look and say" descriptions.

%C 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

%D David Wells, Prime Numbers: The Most Mysterious Figures in Math. Hoboken, New Jersey: John Wiley & Sons (2005): 41

%H Reinhard Zumkeller, <a href="/A056815/b056815.txt">Table of n, a(n) for n = 1..10000</a>

%F A010051(a(n)) * A010051(A045918(a(n))) = 1. - _Reinhard Zumkeller_, Apr 14 2014

%e 193 is prime and its "look and say" description A045918(193) = 111913, is also prime, so 193 belongs to the sequence.

%t LookAndSayA[ n_] := FromDigits@Flatten@((Through[ {Length, First}[ # ] ] &) /@ Split@IntegerDigits@n); Select[Prime@Range[210], PrimeQ@LookAndSayA@# &] (* _Ray Chandler_, Jan 12 2007 *)

%t (* _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): *)

%t LookAndSayA[n_] := FromDigits@Flatten@(IntegerDigits/@Flatten@

%t ((Through[{Length, First}[#]]&)/@Split@IntegerDigits@n)); W=Select[Prime@Range[b, c], PrimeQ@LookAndSayA@#&]

%t (* _Robert G. Wilson v_ then commented (Jan 27 2012) that the following version is cleaner: *)

%t LookAndSayA[n_] := FromDigits@ Flatten@ IntegerDigits@ Flatten[

%t Through[{Length, First}[#]] & /@ Split@ IntegerDigits@ n]

%o (PARI) forprime(p=1,999, isprime(A045918(p)) & print1(p",")) \\ _M. F. Hasler_, Jan 27 2012

%o (Haskell)

%o a056815 n = a056815_list !! (n-1)

%o a056815_list = filter ((== 1) . a010051' . a045918) a000040_list

%o -- _Reinhard Zumkeller_, Apr 14 2014

%Y Cf. A045918, A005150, A127175, A127176.

%Y Cf. A127355.

%K base,nonn

%O 1,1

%A _Joseph L. Pe_, Jan 30 2003

%E Discussion of Mma program added Feb 02 2012 by _N. J. A. Sloane_

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Last modified May 14 03:51 EDT 2021. Contains 343872 sequences. (Running on oeis4.)