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Omni-MATH / For a given positive integer k denote the square of the sum of its digits by f₁(k) and let f_{nplus{}1}(k) equal{} f_1(f_n(k)). Determine the value of f₁₉₉₁(2¹⁹⁹⁰).

Problem

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problem

For a given positive integer k k denote the square of the sum of its digits by f1(k) f_1(k) and let $ f_{n\plus{}1}(k) \equal{} f_1(f_n(k)).$ Determine the value of f1991(21990). f_{1991}(2^{1990}).
Plain-text mathematical notation (without MathML)
For a given positive integer k denote the square of the sum of its digits by f₁(k) and let $ f_{n\plus{}1}(k) \equal{} f_1(f_n(k)).$ Determine the value of f₁₉₉₁(2¹⁹⁹⁰).
Original LaTeX notation
For a given positive integer $ k$ denote the square of the sum of its digits by $ f_1(k)$ and let $ f_{n\plus{}1}(k) \equal{} f_1(f_n(k)).$ Determine the value of $ f_{1991}(2^{1990}).$

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Source and history

task_id
c0cf2ac8-4f09-50c2-90fc-af2351617b81
task_key
test--c0cf2ac8-4f09-50c2-90fc-af2351617b81
task_revision_id
1
config / split
/ test

Official source

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