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A270343
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Numbers k that end with ( sum of digits of k )^2.
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1
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0, 1, 81, 3144, 3256, 6225, 6484, 6576, 7121, 7529, 7676, 9100, 9324, 9361, 9729, 9784, 12144, 12256, 15225, 15484, 15576, 16121, 16529, 16676, 18100, 18324, 18361, 18729, 18784, 21144, 21256, 24225, 24484, 24576, 25121
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listen;
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internal format)
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OFFSET
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1,3
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COMMENTS
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All terms end with a digit from the set S = {0,1,4,5,6,9}.
The sum of the digits of the numbers repeat and also change with regular intervals. For example, the sum of the digits S1 = {12,16,15,22,24,11,23,26,10,18,19,27,28} which is followed by 3144 to 8784, 12144 to 18784, 21144 to 27784, 30144 to 36784. Again S2 = {21,25,15,22,24,11,23,26,10,18,19,27,28} is followed by 39441 to 45784, 48441 to 54784, 57441 to 67784, 66441 to 72784. It can be seen that a set containing 13 elements repeats itself for 4 consecutive ranges.
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LINKS
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EXAMPLE
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For k=3256, sum of digits is 16 and 16^2 is 256.
For k=7121, sum of digits is 11 and 11^2 is 121.
For k=18784, sum of digits is 22 and 22^2 is 484.
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MATHEMATICA
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Select[Range[0, 20000], Function[n, Function[k, If[n >= k, FromDigits@ Take[#, -IntegerLength@ k] == k, False]][Total[#]^2] &@ IntegerDigits@ n]] (* Michael De Vlieger, Mar 15 2016 *)
esdQ[n_]:=Module[{idn=IntegerDigits[n], idn2=IntegerDigits[ Total[ IntegerDigits[ n]]^2]}, Take[ idn, -Length[idn2]]==idn2]; Select[ Range[ 0, 26000], esdQ]//Quiet (* Harvey P. Dale, Jan 01 2022 *)
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PROG
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(PARI) isok(n) = {sds = sumdigits(n)^2; nbs = #Str(sds); ((n - sds) % 10^nbs) == 0; } \\ Michel Marcus, Mar 16 2016
(Python)
for i in range(0, 200000):
res = pow((sum(map(int, str(i)))), 2)
if(i%pow(10, len(str(res)))==res):print(i)
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CROSSREFS
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KEYWORD
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base,nonn,easy
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AUTHOR
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STATUS
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approved
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