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

0,2

Links

Table of n, a(n) for n=0..8.

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

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

Prog

(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

Crossrefs

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

Sequence in context: A084727 A100763 A132538 * A062615 A180162 A129907

Adjacent sequences: A334723 A334724 A334725 * A334727 A334728 A334729

Keyword

nonn,base,more,hard

Author

Giovanni Resta, May 09 2020

Status

approved