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 A343397 Number of ways to write n as 2^x + [y^2/3] + [z^2/4] with x,y,z positive integers, where [.] is the floor function. 10
 0, 1, 2, 3, 4, 4, 5, 5, 8, 5, 9, 5, 8, 8, 6, 9, 9, 10, 8, 11, 10, 10, 9, 9, 14, 8, 8, 10, 12, 11, 6, 14, 13, 10, 12, 13, 15, 11, 13, 9, 20, 6, 12, 17, 13, 13, 10, 11, 17, 12, 11, 13, 15, 14, 9, 13, 13, 14, 11, 18, 11, 15, 7, 12, 22, 13, 14, 17, 17, 11, 15, 13, 24, 16, 9, 17, 15, 15, 14, 18 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Conjecture: a(n) > 0 for all n > 1. We have verified a(n) > 0 for all n = 2..2*10^6. Conjecture verified up to 10^10. - Giovanni Resta, Apr 14 2021 LINKS Zhi-Wei Sun, Table of n, a(n) for n = 1..10000 Zhi-Wei Sun, Natural numbers represented by [x^2/a] + [y^2/b] + [z^2/c], arXiv:1504.01608 [math.NT], 2015. EXAMPLE a(2) = 1 with 2 = 2^1 + [1^2/3] + [1^2/4]. a(3) = 2 with 3 = 2^1 + [1^2/3] + [2^2/4] = 2^1 + [2^2/3] + [1^2/4]. MATHEMATICA PowQ[n_]:=PowQ[n]=n>1&&IntegerQ[Log[2, n]]; tab={}; Do[r=0; Do[If[PowQ[n-Floor[x^2/3]-Floor[y^2/4]], r=r+1], {x, 1, Sqrt[3n-1]}, {y, 1, Sqrt[4(n-Floor[x^2/3]-1)+1]}]; tab=Append[tab, r], {n, 1, 80}]; Print[tab] CROSSREFS Cf. A000079, A000290, A343326, A343368, A343384, A343387, A343391, A343411. Sequence in context: A216411 A110532 A049987 * A270832 A257646 A051898 Adjacent sequences: A343394 A343395 A343396 * A343398 A343399 A343400 KEYWORD nonn AUTHOR Zhi-Wei Sun, Apr 13 2021 STATUS approved

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Last modified June 20 08:48 EDT 2024. Contains 373515 sequences. (Running on oeis4.)