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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
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 (list; graph; refs; listen; history; text; internal format)
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: A019305 A274266 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

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Last modified May 13 19:36 EDT 2021. Contains 343868 sequences. (Running on oeis4.)