Immortal numbers

Immortality of Quaternions

Approximation for various powers at base 10, using immortal Quaternions with 1-2 digits and only positive parts;
2 is subtracted from the amount of integers in order to exclude the super immortal numbers 0 and 1:

$|\mathbb{M}^{power}_{10}|^{\mathbb{H}^{+}}\approx\tfrac{true\ quaternion\ % numbers+pure\ complex\ numbers+integers-2}{{2}^{4}}$

$|\mathbb{M}^{2}_{10}|^{\mathbb{H}^{+}}\approx\tfrac{1432+4+6-2}{{2}^{4}}=90$

$|\mathbb{M}^{3}_{10}|^{\mathbb{H}^{+}}\approx\tfrac{5773+96+13-2}{{2}^{4}}=367.5$

$|\mathbb{M}^{4}_{10}|^{\mathbb{H}^{+}}\approx\tfrac{3769+17+6-2}{{2}^{4}}=236.% 875$

$|\mathbb{M}^{5}_{10}|^{\mathbb{H}^{+}}\approx\tfrac{797580+243+22-2}{{2}^{4}}=% 49865.1875$

$|\mathbb{M}^{6}_{10}|^{\mathbb{H}^{+}}\approx\tfrac{5166+34+14-2}{{2}^{4}}=325% .75$

$|\mathbb{M}^{7}_{10}|^{\mathbb{H}^{+}}\approx\tfrac{188034+100+13-2}{{2}^{4}}=% 11759.0625$

$|\mathbb{M}^{8}_{10}|^{\mathbb{H}^{+}}\approx\tfrac{3232+8+6-2}{{2}^{4}}=202.75$

$|\mathbb{M}^{9}_{10}|^{\mathbb{H}^{+}}\approx\tfrac{999125+274+22-2}{{2}^{4}}=% 62463.6875$

$|\mathbb{M}^{10}_{10}|^{\mathbb{H}^{+}}\approx\tfrac{1856+7+6-2}{{2}^{4}}=116.% 6875$