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A086457
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Both n and n^2 have the same initial digit and also n and n^2 have the same final digit when expressed in base 10.
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6
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0, 1, 10, 11, 95, 96, 100, 101, 105, 106, 110, 111, 115, 116, 120, 121, 125, 126, 130, 131, 135, 136, 140, 141, 895, 896, 950, 951, 955, 956, 960, 961, 965, 966, 970, 971, 975, 976, 980, 981, 985, 986, 990, 991, 995, 996, 1000, 1001, 1005, 1006, 1010, 1011
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| All terms of A045953 appear in this sequence.
Subsequence of A008851; A045953 and A046851 are subsequences. [Reinhard Zumkeller, Jul 27 2011]
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LINKS
| Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
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FORMULA
| A000030(a(n)) = A000030(a(n)^2) and A010879(a(n)) = A010879(a(n)^2).
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EXAMPLE
| a(12) = 115 appears in the sequence because 115*115 = 13225.
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MATHEMATICA
| ldQ[n_]:=Module[{idn=IntegerDigits[n], idn2=IntegerDigits[n^2]}, First[idn]==First[idn2]&&Last[idn]==Last[idn2]]
Select[Range[0, 1100], ldQ] (* From Harvey P. Dale, Feb. 06 2011 *)
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PROG
| (Basic)
left$(str$(n), 1) = left$(str$(n^2), 1) AND right$(str$(n), 1) = right$(str$(n^2), 1)
(Haskell)
a086457 n = a086457_list !! (n-1)
a086457_list = filter (\x -> a000030 x == a000030 (x^2) &&
a010879 x == a010879 (x^2)) [0..]
-- Reinhard Zumkeller, Jul 27 2011
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CROSSREFS
| Cf. A045953, A086458.
Sequence in context: A122602 A037958 A041214 * A046851 A045953 A136830
Adjacent sequences: A086454 A086455 A086456 * A086458 A086459 A086460
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KEYWORD
| base,easy,nonn
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AUTHOR
| Jeremy Gardiner (jeremy.gardiner(AT)btinternet.com), Jul 20 2003
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EXTENSIONS
| Offset corrected by Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 27 2011
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