A377900 After A121053(n) has been found, a(n) is the smallest candidate for A121053(n+1) that has not been eliminated.

1, 1, 1, 6, 6, 9, 9, 9, 12, 12, 12, 15, 15, 15, 18, 18, 18, 21, 21, 21, 24, 24, 24, 26, 26, 28, 28, 32, 32, 32, 32, 34, 34, 36, 36, 39, 39, 39, 42, 42, 42, 45, 45, 45, 48, 48, 48, 50, 50, 52, 52, 55, 55, 55, 57, 57, 60, 60, 60, 63, 63, 63, 65, 65, 68, 68, 68, 70

Offset: 1

Author

N. J. A. Sloane, Nov 14 2024

Keywords

• nonn

Examples

			After a(8) = 9, and A121053(9) = 10 has been determined, the smallest prime not yet used is 17 and the smallest composite not yet used or eliminated is 12 (10 is now eliminated because the terms of A121053 must be distinct), so a(9) = 12.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A099862, A121053, A377898.

Programs

PARI

lista(nn) = my(c=4, t=0); print1("1, 1, 1"); forcomposite(k=4, nn, if(t%2, for(n=c, k-1, print1(", ", k)); c=k); t++); \\ Jinyuan Wang, Nov 29 2024

Python

from sympy import isprime
from itertools import count, islice
def nextcomposite(n): return next(k for k in count(n+1) if not isprime(k))
def agen(): # generator of terms
    yield from [1, 1, 1]
    c, c2 = 4, 6
    for n in count(4):
        if n == c2: c, c2 = c2, nextcomposite(nextcomposite(c2))
        yield c2
print(list(islice(agen(), 70))) # Michael S. Branicky, Nov 29 2024

Formula

a(n) = A099862(k+1) for A099862(k) <= n < A099862(k+1). - Jinyuan Wang, Nov 29 2024

Extensions

More terms from Jinyuan Wang, Nov 29 2024