A334726 a(k) is the earliest start of sequence of exactly k primes generated according to the rules stipulated in A005150.

1, 2, 3, 7, 373, 1223, 233, 19972667609, 75022592087629

Offset: 0

Author

Giovanni Resta, May 09 2020

Keywords

• nonn
• base
• more
• hard

Examples

			The sequence starting at 7 is 7 (prime), 17 (prime), 1117 (prime), and 3117 (composite), so a(3) = 7.
		

Links

• 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.

Crossrefs

Cf. A005150, A079637, A037033, A038131, A038132.

Programs

Python

from sympy import isprime, nextprime
from itertools import count, groupby, islice
def LS(n):
    return int(''.join(str(len(list(g)))+k for k, g in groupby(str(n))))
def f(n): return 0 if not isprime(n) else 1 + f(LS(n))
def agen(startn=0, startk=1):
    n, adict = startn, {i:-1 for i in range(startn)}
    for k in count(startk):
        fk = f(k)
        if fk not in adict: adict[fk] = k
        while n in adict: yield adict[n]; n += 1
print(list(islice(agen(), 7))) # Michael S. Branicky, Jul 27 2022