A364929 - OEIS

%I #112 Jan 31 2024 11:33:00

%S 0,1,3,2,6,11,4,11,19,10,9,35,23,36,22,7,23,40,58,8,28,49,14,192,168,

%T 143,117,90,20,49,79,48,16,49,15,11,13,50,12,51,17,58,100,57,101,56,

%U 102,55,31,20097,37,39,91,38,92,47,45,43,738,679,619,558,496,433,369

%N a(0) = 0; for n > 0, if n appears in the sequence then a(n) is the product of the indices of all previous appearances of n. Otherwise a(n) = a(n-1) - n if nonnegative and not already in the sequence, otherwise a(n) = a(n-1) + n.

%H Michael S. Branicky, <a href="/A364929/b364929.txt">Table of n, a(n) for n = 0..10000</a>

%H David A. Corneth, <a href="/A364929/a364929.gp.txt">PARI program</a>

%e a(2) = 3 = n, thus a(3) = 2.

%e a(5) = 11, as 5 has not previously appeared in the sequence, but a(4) - 5 = 1 has, thus a(5) = a(4) + 5 = 6 + 5 = 11.

%e a(5) and a(7) = 11, and 5 * 7 = 35, thus a(11) = 35.

%o (PARI) See PARI link

%o (Python)

%o from itertools import count, islice

%o def agen(): # generator of terms

%o     an, p = 0, {0: 0} # data list, map of product of indices

%o     for n in count(1):

%o         yield an

%o         an = p[n] if n in p else an+n if an-n < 0 or an-n in p else an-n

%o         p[an] = p[an]*n if an in p else n

%o print(list(islice(agen(), 65))) # _Michael S. Branicky_, Dec 09 2023

%Y Cf. A005132, A340612, A362373.

%K nonn

%O 0,3

%A _Kelvin Voskuijl_, Dec 05 2023

%E More terms from _David A. Corneth_, Dec 09 2023