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.

2, 3, 7, 233, 233, 233, 19972667609, 75022592087629

Offset

0,1

Comments

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.

Links

Table of n, a(n) for n=0..7.

Carlos Rivera, Puzzle 36. Sequences of "descriptive primes", The Prime Puzzles and Problems Connection.

Carlos Rivera, Puzzle 999. In Memoriam to John Horton Conway, The Prime Puzzles and Problems Connection.

Example

233 is the smallest prime p such that p_0 = 233, p_1 = LookAndSay(233) = 1223, p_2 = LookAndSay(1223) = 112213.

Prog

(Python)
from sympy import isprime, nextprime
from itertools import groupby, islice
def LS(n):
    return int(''.join(str(len(list(g)))+k for k, g in groupby(str(n))))
def f(n): return -1 if not isprime(n) else 1 + f(LS(n))
def agen(startn=0, startp=2):
    n, p = startn, startp
    while True:
        fp = f(p)
        while (fp >= n): n += 1; yield p
        p = nextprime(p)
print(list(islice(agen(), 6))) # Michael S. Branicky, Jul 27 2022

Crossrefs

Cf. A045918, A005150.

Sequence in context: A053942 A053954 A063869 * A062662 A084727 A100763

Adjacent sequences: A079634 A079635 A079636 * A079638 A079639 A079640

Keyword

nonn,base,more

Author

Joseph L. Pe, Jan 30 2003

Extensions

Corrected by Mark Hudson (mrmarkhudson(AT)hotmail.com), Feb 02 2003, who reports there are no more terms < 10^6.

a(6) (found by Walter Schneider) and a(7) from Giovanni Resta, May 09 2020

Status

approved