A338216 a(n) is the maximum length of the sequence obtained with the same scheme as in A338134 but starting with n primes.

1, 2, 3, 13, 18, 26, 66, 176, 313, 657, 1022, 2575, 5142, 9269

Offset

1,2

Links

Table of n, a(n) for n=1..14.

Example

a(6) = 26, which is based on the length of the sequence 3, 5, 7, 11, 13, 17, 19, 23, 31, 41, 53, 59, 73, 107, 131, 167, 233, 239, 311, 877, 1277, 1283, 1427, 2393, 3581, 4547.

Prog

(Python)
from sympy import isprime, prime
from itertools import chain, combinations as C
def powerset(s): # skip empty set & singletons
  return chain.from_iterable(C(s, r) for r in range(2, len(s)+1))
def a(n):
  alst, next_set = [prime(i+1) for i in range(1, n)], {prime(n+1)}
  while len(next_set):
    alst.append(min(next_set)); next_set = set()
    for s in powerset(alst[-n:]):
      ss = sum(s)
      if len(next_set):
        if ss > min(next_set): continue
      if ss > alst[-1]:
        if isprime(ss): next_set.add(ss)
  return len(alst) # return alst on a(11) for A338134
for n in range(1, 12):
  print(a(n), end=", ") # Michael S. Branicky, Dec 17 2020

Crossrefs

Cf. A338134 (when n=11).

Sequence in context: A118134 A215386 A352539 * A143871 A225517 A254462

Adjacent sequences: A338213 A338214 A338215 * A338217 A338218 A338219

Keyword

nonn,hard,more

Author

Anthony Winkelspecht, Oct 16 2020

Extensions

a(14) from Michael S. Branicky, Dec 17 2020

Status

approved