A116502 - OEIS

%I #16 Oct 14 2024 18:08:54

%S 69696,56722567225,95540955409,1108033241108033241,

%T 1220096161220096161,4312080784312080784,4432132964432132964,

%U 4880384644880384644,9024307889024307889,9972299169972299169,946308825294630882529,11542927396115429273961,46171709584461717095844

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

%H Giovanni Resta, <a href="/A116502/b116502.txt">Table of n, a(n) for n = 1..300</a>

%H Erich Friedman, <a href="https://erich-friedman.github.io/puzzle/mathpuzzle">Puzzles of the Week</a> [_N. J. A. Sloane_, Mar 12 2011]

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

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

%t 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 *)

%Y Cf. A116500, A116501, A069919.

%K base,nonn

%O 1,1

%A _Giovanni Resta_, Feb 18 2006

%E a(11)-a(13) from _Giovanni Resta_, Aug 01 2018