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A300081
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a(n) is the number of steps needed to reach 1 or 89 under iteration of sum-of-squares-of-digits map.
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2
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0, 5, 7, 4, 4, 9, 5, 5, 6, 1, 6, 5, 2, 6, 6, 3, 5, 5, 4, 5, 5, 6, 3, 6, 3, 5, 6, 3, 2, 7, 2, 3, 6, 4, 5, 8, 2, 3, 7, 4, 6, 6, 4, 4, 7, 4, 5, 6, 4, 4, 6, 3, 5, 7, 5, 4, 6, 1, 4, 9, 3, 5, 8, 4, 4, 7, 2, 2, 8, 5, 5, 6, 2, 5, 6, 2, 9, 8, 3, 5, 5, 3, 3, 6, 1, 2, 8, 10, 0
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OFFSET
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1,2
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COMMENTS
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By the definition, a(1) = a(89) = 0.
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LINKS
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EXAMPLE
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n| 0 1 2 3 4 5 6 7 8 9
-----------------------------------------------------------
2| 2 -> 4 -> 16 -> 37 -> 58 -> 89.
3| 3 -> 9 -> 81 -> 65 -> 61 -> 37 -> 58 -> 89.
4| 4 -> 16 -> 37 -> 58 -> 89.
5| 5 -> 25 -> 29 -> 85 -> 89.
6| 6 -> 36 -> 45 -> 41 -> 17 -> 50 -> 25 -> 29 -> 85 -> 89.
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PROG
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(PARI) f(n) = {my(d = digits(n)); sum(k=1, #d, d[k]^2); }
a(n) = {my(nb = 0, fn = n); while (! ((n == 1) || (n == 89)), n = f(n); nb++); nb; } \\ Michel Marcus, Feb 25 2018
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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