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A118881
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Square of sum of decimal digits of n.
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10
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0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 36, 49, 64, 81, 100, 121, 144
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OFFSET
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0,3
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COMMENTS
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a(k) = k iff k = 0, 1, 81; also, the only solution to the double equation a(k) = m and a(m) = k with k < m is (169, 256) (proof in Diophante link, 2ème jonglerie). - Bernard Schott, Mar 08 2021
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LINKS
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FORMULA
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EXAMPLE
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Trajectories of the map x->a(x), A177148:
1 ->1 ->1 ->1 ->1 ->1 ->1 ->1 ->1 ->...
2 ->4 ->16 ->49 ->169 ->256 ->169 ->256 ->169 ->...
3 ->9 ->81 ->81 ->81 ->81 ->81 ->81 ->81 ->...
4 ->16 ->49 ->169 ->256 ->169 ->256 ->169 ->256 ->...
5 ->25 ->49 ->169 ->256 ->169 ->256 ->169 ->256 ->...
6 ->36 ->81 ->81 ->81 ->81 ->81 ->81 ->81 ->...
7 ->49 ->169 ->256 ->169 ->256 ->169 ->256 ->169 ->...
8 ->64 ->100 ->1 ->1 ->1 ->1 ->1 ->1 ->... (End)
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MAPLE
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read("transforms") :
digsum(n)^2 ;
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MATHEMATICA
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Table[Total[IntegerDigits[n]]^2, {n, 0, 70}] (* Harvey P. Dale, Jul 31 2012 *)
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PROG
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(Python)
def a(n): return sum(map(int, str(n)))**2
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CROSSREFS
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KEYWORD
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base,easy,nonn
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AUTHOR
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STATUS
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approved
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