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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: 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

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Last modified July 12 10:18 EDT 2024. Contains 374244 sequences. (Running on oeis4.)