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A079637 Smallest prime p with audioactive "echo" of at least n, that is, the finite sequence p_0 = p, p_1 = LookAndSay(p_0), ..., p_n = LookAndSay(p_(n-1)) consists entirely of primes.

%I A079637 #22 Jul 27 2022 02:44:27
%S A079637 2,3,7,233,233,233,19972667609,75022592087629
%N A079637 Smallest prime p with audioactive "echo" of at least n, that is, the finite sequence p_0 = p, p_1 = LookAndSay(p_0), ..., p_n = LookAndSay(p_(n-1)) consists entirely of primes.
%C A079637 LookAndSay(n) denotes the description of the digits of n. For example, LookAndSay(111223) = 312213. 2. There is no prime < 10^5 with echo = 6.
%H A079637 Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_036.htm">Puzzle 36. Sequences of "descriptive primes"</a>, The Prime Puzzles and Problems Connection.
%H A079637 Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_999.htm">Puzzle 999. In Memoriam to John Horton Conway</a>, The Prime Puzzles and Problems Connection.
%e A079637 233 is the smallest prime p such that p_0 = 233, p_1 = LookAndSay(233) = 1223, p_2 = LookAndSay(1223) = 112213.
%o A079637 (Python)
%o A079637 from sympy import isprime, nextprime
%o A079637 from itertools import groupby, islice
%o A079637 def LS(n):
%o A079637     return int(''.join(str(len(list(g)))+k for k, g in groupby(str(n))))
%o A079637 def f(n): return -1 if not isprime(n) else 1 + f(LS(n))
%o A079637 def agen(startn=0, startp=2):
%o A079637     n, p = startn, startp
%o A079637     while True:
%o A079637         fp = f(p)
%o A079637         while (fp >= n): n += 1; yield p
%o A079637         p = nextprime(p)
%o A079637 print(list(islice(agen(), 6))) # _Michael S. Branicky_, Jul 27 2022
%Y A079637 Cf. A045918, A005150.
%K A079637 nonn,base,more
%O A079637 0,1
%A A079637 _Joseph L. Pe_, Jan 30 2003
%E A079637 Corrected by Mark Hudson (mrmarkhudson(AT)hotmail.com), Feb 02 2003, who reports there are no more terms < 10^6.
%E A079637 a(6) (found by Walter Schneider) and a(7) from _Giovanni Resta_, May 09 2020