A304935 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.

1, 0, 0, 5, 11, 6, 71, 19, 123, 33, 174, 426, 174, 233, 625, 816, 5695, 3656, 15936, 246960, 24234, 24234, 35151, 140604, 177399, 250982, 1304130, 1304130, 1304130, 1304130, 5532955, 5532955, 58136459, 8525544, 8525544, 58136459, 941988492, 58136459, 941988492

Offset

1,4

Comments

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

Links

Table of n, a(n) for n=1..39.

Rémy Sigrist, PARI program for A304935

Example

a(2) = a(3) = 0, since no positive squares are achievable.
Some examples:
a(7) = 71 = sqrt(0+1+2*3*4*5*6*7).
a(8) = 19 = sqrt(0+1*2+3+4*5+6*7*8).
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)

Mathematica

sqStrTest[n_] := Module[{bVal, bStr, i, j, iB, mVal, mStr},
  bVal = -1;
  For[i = 0, i < 2^n, i++,
   iB = IntegerDigits[i, 2];
   While[Length[iB] < n, PrependTo[iB, 0]];
   mStr = "0";
   For[j = 1, j <= n, j++,
    mStr = StringJoin[mStr, If[iB[[j]] == 0, "+", "*"], ToString[j]]];
   mVal = ToExpression[mStr];
   If[Sqrt[mVal] == Floor[Sqrt[mVal]],
    If[mVal > bVal, {bVal, bStr} = {mVal, mStr}]
    ]
   ];
  Print[{Sqrt[bVal], bVal, bStr}]]

Prog

(PARI) See Links section.

Crossrefs

Upper-bounded by sqrt(A038507).

Sequence in context: A274266 A365726 A318259 * A156274 A079778 A172183

Adjacent sequences: A304932 A304933 A304934 * A304936 A304937 A304938

Keyword

nonn

Author

Andy Niedermaier, May 21 2018

Extensions

More terms from Rémy Sigrist, May 22 2018

Status

approved