A238712 Numbers in which squares may end (in base 10).

0, 1, 4, 5, 6, 9, 16, 21, 24, 25, 29, 36, 41, 44, 49, 56, 61, 64, 69, 76, 81, 84, 89, 96, 100, 104, 116, 121, 124, 129, 136, 144, 156, 161, 164, 169, 176, 184, 196, 201, 204, 209, 216, 224, 225, 236, 241, 244, 249, 256, 264, 276, 281, 284, 289, 296, 304

Offset: 1

Author

M. F. Hasler, Mar 03 2014

Keywords

• nonn
• base

Comments

The union of "squares mod 10" (= the first 6 terms) and "squares mod 100" (A010461) and "squares mod 1000" (A122986) etc.

The number of terms < 10^k beginning with k=0: 1, 6, 24, 165, 1101, 9306, 79620, 753462, 7198791, 70919559, ... - Robert G. Wilson v, Sep 04 2014

Examples

			6 is in the sequence because 4^2 = 16 ends in the digit 6.
7 is not in the sequence because no square can end with the digit 7.
		

Links

• Derek Orr, Table of n, a(n) for n = 1..9306

Crossrefs

Cf. A161355, A246422, A246448 (Complement).

Programs

Mathematica

mx = 3; t = Union@ Table[ Mod[n^2, 10^mx], {n, 10^mx/2}]; t = Union@ Flatten@ Table[ Mod[t, 10^m], {m, mx}] (* Robert G. Wilson v, Sep 04 2014 *)

PARI

a=[];for(m=1,3,a=setunion(a,Set(vector(10^m,n,n^2)%10^m)));a

Formula

If n is present so is n^2. - Robert G. Wilson v, Sep 04 2014