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A371295 Value k at the n-th step of A371282, where multiplied values are positive and subtracted values are negative.

%I A371295 #16 Mar 19 2024 08:32:15
%S A371295 2,3,-1,4,-17,5,-11,6,-16,7,-49,9,-54,8,-62,10,-89,12,-120,13,-143,14,
%T A371295 -168,15,-194,18,-271,19,-305,20,-341,21,-378,22,-440,23,-483,24,-527,
%U A371295 25,-599,26,-649,27,-701,28,-755,29,-811,30,-869,31,-929,32,-991,33
%N A371295 Value k at the n-th step of A371282, where multiplied values are positive and subtracted values are negative.
%H A371295 Michael S. Branicky, <a href="/A371295/b371295.txt">Table of n, a(n) for n = 1..10000</a>
%e A371295 At the first step of A371282, to get from A371282(1)=1 to A371282(2)=2, we multiply by 2, so a(1)=2.
%e A371295 At the fifth step of A371282, to get from A371282(5)=20 to A371282(6)=3, we subtract 17, so a(5)=-17.
%o A371295 (Python)
%o A371295 from itertools import islice
%o A371295 def agen(): # generator of terms
%o A371295     mina, an, aset, mink, kset = 1, 1, {1}, 1, set()
%o A371295     while True:
%o A371295         k1, ak1, k2 = 0, mina, mink
%o A371295         if mina < an:
%o A371295             for ak1 in range(mina, an-mink+1):
%o A371295                 if ak1 not in aset and an - ak1 not in kset:
%o A371295                     k1 = an - ak1
%o A371295                     break
%o A371295         while k2 in kset or an*k2 in aset:
%o A371295             k2 += 1
%o A371295         an, k = (an-k1, k1) if k1 > 0 else (an*k2, k2)
%o A371295         yield -k if k1 > 0 else k
%o A371295         aset.add(an)
%o A371295         kset.add(k)
%o A371295         while mina in aset: mina += 1
%o A371295         while mink in kset: mink += 1
%o A371295 print(list(islice(agen(), 56))) # _Michael S. Branicky_, Mar 18 2024
%Y A371295 Cf. A371282, A099004 (steps of add or subtract), A360597 (steps of multiply or divide).
%K A371295 sign
%O A371295 1,1
%A A371295 _Neal Gersh Tolunsky_, Mar 17 2024
%E A371295 a(12) and beyond from _Michael S. Branicky_, Mar 18 2024