A086539 Beginning with 1, a(n) = smallest number > a(n-1) and coprime to the k previous terms, where k = floor(n/2).

1, 2, 3, 5, 7, 8, 9, 11, 13, 17, 19, 23, 25, 28, 29, 31, 33, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 80, 83, 89, 91, 97, 101, 103, 107, 109, 111, 113, 121, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 230, 233

Offset

1,2

Comments

Includes all primes. - Robert Israel, Jun 17 2024

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(7) = 9 which is coprime to the three previous terms 5, 7 and 8.

Maple

R:= 1, 2: x:= 2:
for n from 3 to 100 do
  t:= ilcm(R[ceil(n/2) .. n-1]);
  for i from x+1 while igcd(i, t) <> 1 do od:
  R:= R, i;
  x:= i;
od:
R; # Robert Israel, Jun 23 2024

Prog

(Python)
from math import gcd, lcm
from itertools import count, islice
def agen(): # generator of terms
    alst, an, LCM,  = [1], 1, 1
    for n in count(2):
        yield an
        LCM = lcm(*alst[-(n//2):])
        an = next(k for k in count(an+1) if gcd(k, LCM) == 1)
        alst.append(an)
print(list(islice(agen(), 62))) # Michael S. Branicky, Jun 25 2024

Crossrefs

Sequence in context: A144100 A359059 A328320 * A171217 A344591 A049468

Adjacent sequences: A086536 A086537 A086538 * A086540 A086541 A086542

Keyword

nonn

Author

Amarnath Murthy, Aug 29 2003

Extensions

More terms from David Wasserman, Mar 21 2005

Definition and offset corrected by Robert Israel, Jun 17 2024

Status

approved