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

%I A145198 #21 Sep 01 2025 18:02:43
%S A145198 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,
%T A145198 30,31,32,33,34,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,
%U A145198 54,55,57,58,59,61,62,63,64,65,66,67,68,69,70,71,73,74,75,76,77,78,79,80
%N A145198 a(n) is the least number not already in the sequence and not the product of consecutive terms in the sequence.
%H A145198 Rémy Sigrist, <a href="/A145198/b145198.txt">Table of n, a(n) for n = 1..10000</a>
%o A145198 (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
%o A145198 (HP 49G)
%o A145198 HP 49G calculator program from _Gerald Hillier_, Oct 24 2008
%o A145198 << 0 OVER NDUPN
%o A145198 ->LIST DUPDUP + 1 0
%o A145198 0 -> M V U K J P
%o A145198 << 1 M
%o A145198 FOR N K
%o A145198 WHILE U OVER
%o A145198 GET
%o A145198 REPEAT 1 +
%o A145198 END 'K' STO V
%o A145198 N K PUT 'V' STO U K
%o A145198 1 PUT N 1 - 'J' STO
%o A145198 K 'P' STO
%o A145198 WHILE J 0 >
%o A145198 IF
%o A145198 THEN P V J
%o A145198 GET * DUP 'P' STO M
%o A145198 2 * <=
%o A145198 ELSE 0
%o A145198 END
%o A145198 REPEAT P 1
%o A145198 PUT J 1 - 'J' STO
%o A145198 END 'U' STO
%o A145198 NEXT V
%o A145198 >>
%o A145198 >>
%o A145198 (Python)
%o A145198 from operator import mul
%o A145198 from itertools import count, accumulate, islice
%o A145198 from collections import deque
%o A145198 def A145198_gen(): # generator of terms
%o A145198     aset, alist = set(), deque()
%o A145198     for k in count(1):
%o A145198         if k in aset:
%o A145198             aset.remove(k)
%o A145198         else:
%o A145198             yield k
%o A145198             aset |= set(k*d for d in accumulate(alist,mul))
%o A145198             alist.appendleft(k)
%o A145198 A145198_list = list(islice(A145198_gen(),50)) # _Chai Wah Wu_, Sep 01 2025
%Y A145198 Cf. A002048, A145278 (complement).
%K A145198 nonn,changed
%O A145198 1,2
%A A145198 _Gerald Hillier_, Oct 04 2008
%E A145198 Extended by _Klaus Brockhaus_, Oct 06 2008