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a(1) = 1; for n > 1, a(n) is the least positive integer not already in the sequence such that a(n) == a(n-1) (mod A004280(n)).
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%I #21 Mar 06 2024 00:57:29

%S 1,3,6,11,4,13,2,15,30,47,9,51,5,55,28,57,26,59,24,61,22,63,20,65,18,

%T 67,16,69,14,71,12,73,10,75,8,77,148,221,146,223,144,225,142,227,53,

%U 231,49,235,45,239,41,243,37,247,33,251,29,255,25,259,21,263,17,267,140,269,7,273,138,275,136,277,134,279,132,281

%N a(1) = 1; for n > 1, a(n) is the least positive integer not already in the sequence such that a(n) == a(n-1) (mod A004280(n)).

%C Analogous to A364054, but whereas that sequence is based on the sequence of primes (2, 3, 5, 7, 11, ....), the present sequence is based on the sequence 2, 3, 5, 7, 9, 11, 13, 15, ... (2 together with the odd numbers >1, essentially A004280).

%H N. J. A. Sloane, <a href="/A368382/b368382.txt">Table of n, a(n) for n = 1..10000</a>

%o (Python)

%o from itertools import count, islice

%o def A368382_gen(): # generator of terms

%o a, aset, p = 1, {0,1}, 2

%o while True:

%o yield a

%o for b in count(a%p,p):

%o if b not in aset:

%o aset.add(b)

%o a, p = b, 3 if p == 2 else p+2

%o break

%o A368382_list = list(islice(A368382_gen(),40)) # _Chai Wah Wu_, Mar 05 2024

%Y Cf. A004280.

%Y Similar definitions: A005132, A006509, A364054.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Mar 03 2024