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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, 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
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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 14 2024
EXTENSIONS
More terms from Jinyuan Wang, Nov 29 2024
STATUS
approved