A116502 Squares with structure dmdmd, where d is a single digit and m a string of digits.

69696, 56722567225, 95540955409, 1108033241108033241, 1220096161220096161, 4312080784312080784, 4432132964432132964, 4880384644880384644, 9024307889024307889, 9972299169972299169, 946308825294630882529, 11542927396115429273961, 46171709584461717095844

Offset: 1

Author

Giovanni Resta, Feb 18 2006

Keywords

• base
• nonn

Examples

			309097^2 = a(3) = 9[5540]9[5540]9.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..300
• Erich Friedman, Puzzles of the Week [_N. J. A. Sloane_, Mar 12 2011]

Crossrefs

Cf. A116500, A116501, A069919.

Programs

Mathematica

w={}; Do[s = Reduce[(1 + 10^(1+e) + 100^(1+e)) d + 10 (1+10^(1+e)) x == y^2 && 0 <= x < 10^e && y>0, {x,y}, Integers]; If[s =!= False, w = Union[w, y^2 /. List@ ToRules@ s]], {e, 12}, {d, 9}]; w (* Giovanni Resta, Aug 01 2018 *)

Formula

a(n) = A116501(n)^2.

Extensions

a(11)-a(13) from Giovanni Resta, Aug 01 2018