A304935 - OEIS

%I #19 Jun 25 2018 02:57:35

%S 1,0,0,5,11,6,71,19,123,33,174,426,174,233,625,816,5695,3656,15936,

%T 246960,24234,24234,35151,140604,177399,250982,1304130,1304130,

%U 1304130,1304130,5532955,5532955,58136459,8525544,8525544,58136459,941988492,58136459,941988492

%N a(n) is the largest possible integer value for sqrt(0 _ 1 _ 2 _ ... _ n), where one is allowed to place any mixture of +'s and *'s in the n blank spaces.

%C Inspired by a test ARML problem from 2018, which asked students to determine a(8).

%H Rémy Sigrist, <a href="/A304935/a304935.gp.txt">PARI program for A304935</a>

%e a(2) = a(3) = 0, since no positive squares are achievable.

%e Some examples:

%e a(7) = 71 = sqrt(0+1+2*3*4*5*6*7).

%e a(8) = 19 = sqrt(0+1*2+3+4*5+6*7*8).

%e a(20) = 246960 = sqrt(0+1*2*3*4*5*6*7*8*9*10*11+12*13*14*15*16*17*18*19*20)

%t sqStrTest[n_] := Module[{bVal, bStr, i, j, iB, mVal, mStr},

%t   bVal = -1;

%t   For[i = 0, i < 2^n, i++,

%t    iB = IntegerDigits[i, 2];

%t    While[Length[iB] < n, PrependTo[iB, 0]];

%t    mStr = "0";

%t    For[j = 1, j <= n, j++,

%t     mStr = StringJoin[mStr, If[iB[[j]] == 0, "+", "*"], ToString[j]]];

%t    mVal = ToExpression[mStr];

%t    If[Sqrt[mVal] == Floor[Sqrt[mVal]],

%t     If[mVal > bVal, {bVal, bStr} = {mVal, mStr}]

%t     ]

%t    ];

%t   Print[{Sqrt[bVal], bVal, bStr}]]

%o (PARI) See Links section.

%Y Upper-bounded by sqrt(A038507).

%K nonn

%O 1,4

%A _Andy Niedermaier_, May 21 2018

%E More terms from _Rémy Sigrist_, May 22 2018