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A245584
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Let f(m) put the leftmost digit of the positive integer m at its end; a(n) is the sequence of all positive integers m with f^2(m)=f(m^2).
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1
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1, 2, 3, 12, 122, 1222, 12222, 122222, 1222222, 12222222, 122222222
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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LINKS
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FORMULA
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One can easily prove that all integers of the form 12...2 are elements of the sequence.
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EXAMPLE
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122^2=14884 and 221^2=48841.
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MATHEMATICA
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f[m_Integer] := Module[{w}, w := IntegerDigits[m]; FromDigits[Rest[AppendTo[w, First[w]]]]]; a245584[n_Integer] :=
Select[Range[n], If[f[#]^2 == f[#^2] && ! Mod[#, 10] == 0, True, False] &]; a245584[10^5] (* Michael De Vlieger, Aug 17 2014 *)
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PROG
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(Python)
import math
max = 10000
print('los')
for n in range(1, max):
nst = str(n*n)
nnewst = nst[1:] + nst[0]
d = int(nnewst)
e = int(math.sqrt(d))
est = str(e)
enewst = est[len(est)-1] + est[:len(est)-1]
if (e * e == d) and (nnewst[0] != "0") and (str(n) == enewst):
print(n, ' ', e)
print('End.')
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CROSSREFS
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KEYWORD
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nonn,base,more
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AUTHOR
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STATUS
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approved
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