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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 (list; graph; refs; listen; history; text; internal format)
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

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

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

Cf. A045953, A086458.

Sequence in context: A041214 A228381 A262229 * A046851 A045953 A136830

Adjacent sequences:  A086454 A086455 A086456 * A086458 A086459 A086460

KEYWORD

base,easy,nonn

AUTHOR

Jeremy Gardiner, Jul 20 2003

EXTENSIONS

Offset corrected by Reinhard Zumkeller, Jul 27 2011

STATUS

approved

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Last modified March 29 18:39 EDT 2017. Contains 284273 sequences.