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A086457
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.
6
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
OFFSET
1,3
COMMENTS
All terms of A045953 appear in this sequence.
Subsequence of A008851; A045953 and A046851 are subsequences. [Reinhard Zumkeller, Jul 27 2011]
Intersection of A008851 and A089951. - Michel Marcus, Mar 19 2015
LINKS
FORMULA
A000030(a(n)) = A000030(a(n)^2) and A010879(a(n)) = A010879(a(n)^2).
EXAMPLE
a(12) = 115 appears in the sequence because 115*115 = 13225.
MATHEMATICA
ldQ[n_]:=Module[{idn=IntegerDigits[n], idn2=IntegerDigits[n^2]}, First[ idn] == First[idn2]&&Last[idn]==Last[idn2]]; Select[Range[ 0, 1100], ldQ] (* Harvey P. Dale, Feb. 06 2011 *)
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
CROSSREFS
Sequence in context: A262229 A347182 A331604 * A046851 A045953 A136830
KEYWORD
base,easy,nonn
AUTHOR
Jeremy Gardiner, Jul 20 2003
EXTENSIONS
Offset corrected by Reinhard Zumkeller, Jul 27 2011
STATUS
approved