A297839 Numbers k > 0 that set a new record for the closeness of (4/3)*Pi*k^3 to an integer.
1, 3, 4, 14, 18, 23, 62, 95, 423, 5339, 12352, 108359, 129805, 5334194, 82007322, 90401717, 199671691, 434184265, 655956850, 44438886071
Offset: 1
Examples
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...
Links
- David Consiglio, Jr., Python Program
- Sean A. Irvine, Java program (github)
Programs
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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++)
Extensions
a(15)-a(19) from Jon E. Schoenfield, Jan 07 2018
a(20) from David Consiglio, Jr., Mar 14 2023
Comments