A145198 a(n) is the least number not already in the sequence and not the product of consecutive terms in the sequence.

1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 80

Offset: 1

Author

Gerald Hillier, Oct 04 2008

Keywords

• nonn
• changed

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002048, A145278 (complement).

Programs

PARI

{m=72; v=vector(m); z=2*m; u=vectorsmall(z); k=1; for(n=1, m, while(u[k], k++); v[n]=k; u[k]=1; j=n-1; p=k; while(j>0&&(p=p*v[j])<=z, u[p]=1; j--)); for(i=1, m, print1(v[i], ","))} \\ Klaus Brockhaus, Oct 06 2008
(HP 49G)
HP 49G calculator program from Gerald Hillier, Oct 24 2008
<< 0 OVER NDUPN
->LIST DUPDUP + 1 0
0 -> M V U K J P
<< 1 M
FOR N K
WHILE U OVER
GET
REPEAT 1 +
END 'K' STO V
N K PUT 'V' STO U K
1 PUT N 1 - 'J' STO
K 'P' STO
WHILE J 0 >
IF
THEN P V J
GET * DUP 'P' STO M
2 * <=
ELSE 0
END
REPEAT P 1
PUT J 1 - 'J' STO
END 'U' STO
NEXT V
>>
>>

Python

from operator import mul
from itertools import count, accumulate, islice
from collections import deque
def A145198_gen(): # generator of terms
    aset, alist = set(), deque()
    for k in count(1):
        if k in aset:
            aset.remove(k)
        else:
            yield k
            aset |= set(k*d for d in accumulate(alist,mul))
            alist.appendleft(k)
A145198_list = list(islice(A145198_gen(),50)) # Chai Wah Wu, Sep 01 2025

Extensions

Extended by Klaus Brockhaus, Oct 06 2008