cp's OEIS Frontend

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.

%I A086457 #24 Jun 29 2025 21:24:14
%S A086457 0,1,10,11,95,96,100,101,105,106,110,111,115,116,120,121,125,126,130,
%T A086457 131,135,136,140,141,895,896,950,951,955,956,960,961,965,966,970,971,
%U A086457 975,976,980,981,985,986,990,991,995,996,1000,1001,1005,1006,1010,1011
%N 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.
%C A086457 All terms of A045953 appear in this sequence.
%C A086457 Subsequence of A008851; A045953 and A046851 are subsequences. [_Reinhard Zumkeller_, Jul 27 2011]
%C A086457 Intersection of A008851 and A089951. - _Michel Marcus_, Mar 19 2015
%H A086457 Reinhard Zumkeller, <a href="/A086457/b086457.txt">Table of n, a(n) for n = 1..10000</a>
%F A086457 A000030(a(n)) = A000030(a(n)^2) and A010879(a(n)) = A010879(a(n)^2).
%e A086457 a(12) = 115 appears in the sequence because 115*115 = 13225.
%t A086457 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 *)
%o A086457 (BASIC)
%o A086457 left$(str$(n), 1) = left$(str$(n^2), 1) AND right$(str$(n), 1) = right$(str$(n^2), 1)
%o A086457 (Haskell)
%o A086457 a086457 n = a086457_list !! (n-1)
%o A086457 a086457_list = filter (\x -> a000030 x == a000030 (x^2) &&
%o A086457                              a010879 x == a010879 (x^2)) [0..]
%o A086457 -- _Reinhard Zumkeller_, Jul 27 2011
%Y A086457 Cf. A045953, A086458.
%K A086457 base,easy,nonn
%O A086457 1,3
%A A086457 _Jeremy Gardiner_, Jul 20 2003
%E A086457 Offset corrected by _Reinhard Zumkeller_, Jul 27 2011