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

2, 3, -1, 4, -17, 5, -11, 6, -16, 7, -49, 9, -54, 8, -62, 10, -89, 12, -120, 13, -143, 14, -168, 15, -194, 18, -271, 19, -305, 20, -341, 21, -378, 22, -440, 23, -483, 24, -527, 25, -599, 26, -649, 27, -701, 28, -755, 29, -811, 30, -869, 31, -929, 32, -991, 33

Offset: 1

Author

Neal Gersh Tolunsky, Mar 17 2024

Keywords

• sign

Examples

			At the first step of A371282, to get from A371282(1)=1 to A371282(2)=2, we multiply by 2, so a(1)=2.
At the fifth step of A371282, to get from A371282(5)=20 to A371282(6)=3, we subtract 17, so a(5)=-17.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A371282, A099004 (steps of add or subtract), A360597 (steps of multiply or divide).

Programs

Python

from itertools import islice
def agen(): # generator of terms
    mina, an, aset, mink, kset = 1, 1, {1}, 1, set()
    while True:
        k1, ak1, k2 = 0, mina, mink
        if mina < an:
            for ak1 in range(mina, an-mink+1):
                if ak1 not in aset and an - ak1 not in kset:
                    k1 = an - ak1
                    break
        while k2 in kset or an*k2 in aset:
            k2 += 1
        an, k = (an-k1, k1) if k1 > 0 else (an*k2, k2)
        yield -k if k1 > 0 else k
        aset.add(an)
        kset.add(k)
        while mina in aset: mina += 1
        while mink in kset: mink += 1
print(list(islice(agen(), 56))) # Michael S. Branicky, Mar 18 2024

Extensions

a(12) and beyond from Michael S. Branicky, Mar 18 2024