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.

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

Author

Jeremy Gardiner, Jul 20 2003

Keywords

• base
• easy
• nonn

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

Examples

			a(12) = 115 appears in the sequence because 115*115 = 13225.
		

Links

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

Crossrefs

Cf. A045953, A086458.

Programs

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

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 *)

Formula

A000030(a(n)) = A000030(a(n)^2) and A010879(a(n)) = A010879(a(n)^2).

Extensions

Offset corrected by Reinhard Zumkeller, Jul 27 2011