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 A297839 Numbers k > 0 that set a new record for the closeness of (4/3)*Pi*k^3 to an integer. 2
 1, 3, 4, 14, 18, 23, 62, 95, 423, 5339, 12352, 108359, 129805, 5334194, 82007322, 90401717, 199671691, 434184265, 655956850, 44438886071 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Integer radii such that the volume of the corresponding sphere is closer to an integer than for any smaller integer radius. LINKS Table of n, a(n) for n=1..20. David Consiglio, Jr., Python Program Sean A. Irvine, Java program (github) EXAMPLE k | (4/3)*Pi*k^3 | Deviation from integer --------------------------------------------------------------------------- 1 | 4.188790204786390... | 0.188790204786390... 3 | 113.097335529232556... | 0.097335529232556... 4 | 268.082573106329023... | 0.082573106329023... 14 | 11494.040321933856861... | 0.040321933856861... 18 | 24429.024474314232222... | 0.024474314232222... 23 | 50965.010421636019109... | 0.010421636019109... 62 | 998305.991926330990581... | 0.008073669009418... 95 | 3591364.001828731970435... | 0.001828731970435... 423 | 317036825.999590816501793... | 0.000409183498206... 5339 | 637482653747.999839504336479... | 0.000160495663520... 12352 | 7894060641354.000003942767448... | 0.000003942767448... 108359 | 5329464512150064.999997849950689... | 0.000000215004931... 129805 | 9161421693208264.000000035388795... | 0.000000035388795... 5334194 | 635762677398025211698.999999995151941... | 0.000000004848058... PROG (PARI) closeness(n) = my(v=(4/3)*Pi*n^3); if(round(v) > v, return(round(v)-v), return(v-round(v))) my(r=1, k=1, c=0); while(1, c=closeness(k); if(c < r, print1(k, ", "); r=c); k++) CROSSREFS Cf. A066645, A135973, A254714, A297840. Sequence in context: A282604 A281524 A299040 * A279938 A280331 A079274 Adjacent sequences: A297836 A297837 A297838 * A297840 A297841 A297842 KEYWORD nonn,hard,more AUTHOR Felix Fröhlich, Jan 07 2018 EXTENSIONS a(15)-a(19) from Jon E. Schoenfield, Jan 07 2018 a(20) from David Consiglio, Jr., Mar 14 2023 STATUS approved

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Last modified July 18 06:54 EDT 2024. Contains 374377 sequences. (Running on oeis4.)