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A056815 Primes with prime "look and say" descriptions. 11
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
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
REFERENCES
David Wells, Prime Numbers: The Most Mysterious Figures in Math. Hoboken, New Jersey: John Wiley & Sons (2005): 41.
LINKS
FORMULA
A010051(a(n)) * A010051(A045918(a(n))) = 1. - Reinhard Zumkeller, Apr 14 2014
EXAMPLE
193 is prime and its "look and say" description A045918(193) = 111913, is also prime, so 193 belongs to the sequence.
MATHEMATICA
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]
PROG
(PARI) forprime(p=1, 999, isprime(A045918(p)) & print1(p", ")) \\ M. F. Hasler, Jan 27 2012
(Haskell)
a056815 n = a056815_list !! (n-1)
a056815_list = filter ((== 1) . a010051' . a045918) a000040_list
-- Reinhard Zumkeller, Apr 14 2014
(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)))
print(list(islice(agen(), 51))) # Michael S. Branicky, Feb 03 2023
CROSSREFS
Cf. A127355.
Sequence in context: A339943 A127355 A079470 * A127176 A100343 A085396
KEYWORD
base,nonn
AUTHOR
Joseph L. Pe, Jan 30 2003
EXTENSIONS
Discussion of Mma program added Feb 02 2012 by N. J. A. Sloane
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)