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

1,4

Links

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

Formula

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

Example

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.

Prog

(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

Crossrefs

Cf. A099862, A121053, A377898.

Sequence in context: A337607 A379468 A198115 * A291545 A205372 A301690

Adjacent sequences: A377897 A377898 A377899 * A377901 A377902 A377903

Keyword

nonn

Author

N. J. A. Sloane, Nov 14 2024

Extensions

More terms from Jinyuan Wang, Nov 29 2024

Status

approved