cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A380111 a(n) is the least number whose fourth power is an n-digit fourth power which has the maximum sum of digits (A373914(n)).

Original entry on oeis.org

1, 3, 4, 8, 16, 26, 47, 74, 118, 308, 518, 659, 1768, 2868, 5396, 8256, 14482, 28871, 55368, 97063, 147768, 228558, 562341, 835718, 1727156, 2878406, 5458722, 8175708, 16234882, 27831542, 53129506, 98665756, 166025442, 315265896, 510466356, 904245732, 1188893858, 2298249374, 5106312756
Offset: 1

Views

Author

Zhining Yang, Jan 12 2025

Keywords

Examples

			a(7) = 47 because among all 7-digit fourth powers, 47^4=487968 is the least one (another larger is 56^4=9834496) which has the maximum sum of digits, 43 = A373914(7).
		

Crossrefs

Other powers: A379869, A379650, A380567.

Programs

  • C
    /* See A373914. */
  • Mathematica
    Table[t=SortBy[Map[{#,Total@IntegerDigits[#^4]}&,Range[Ceiling[10^((n-1)/4)],Floor[(10^n-1)^(1/4)]]],Last];
    Select[t,#[[2]]==t[[-1]][[2]]&][[1,1]],{n,24}]

A380566 a(n) = k is the largest k for which k^5 is n digits long and the sum of digits of k^5 is the maximum for any n digit 5th power (A374025).

Original entry on oeis.org

1, 2, 3, 6, 9, 15, 18, 37, 58, 93, 156, 179, 368, 579, 756, 1379, 2337, 3965, 6006, 9746, 14198, 25046, 38779, 60006, 98746, 151446, 231755, 389658, 585516, 819199, 1584779, 2452779, 3897999, 5400759, 9744998, 15517759, 23936959, 28737498, 62943519, 95635199, 156373159, 225142779, 351816939, 595519999
Offset: 1

Views

Author

Zhining Yang, Jan 26 2025

Keywords

Examples

			a(14) = 579 because among all 14-digit fifth powers(399^5-630^5), 549^5=49872566977749,579^5=65071799758899, both have the maximum sum of digits, 90 = A374025(14) and 579 is the largest.
		

Crossrefs

Programs

  • Mathematica
    a[n_]:=Module[{m=Floor[(10^n-1)^(1/5)],max=0},For[k=m,k>=Ceiling[10^((n-1)/5)],k--,t=Total@IntegerDigits[k^5];If[t>max,s=k;max=t]];s];Table[a[n],{n,30}]

A379869 a(n) is the least number whose cube is an n-digit cube which has the maximum sum of digits (A373727(n)).

Original entry on oeis.org

2, 4, 9, 19, 31, 92, 157, 423, 927, 1966, 4289, 8782, 12599, 30355, 99829, 215083, 341075, 989353, 2131842, 4081435, 8334082, 20632999, 43967926, 88316866, 190349299, 364929616, 735501679, 1948602829, 3036548692, 9654499999, 17087193298, 31037622999, 99594689449, 181610950229, 426932901019, 956829383603
Offset: 1

Views

Author

Zhining Yang, Jan 11 2025

Keywords

Examples

			For n=7, the maximum sum of digits for a 7-digit cube is A373727(7) = 46 and this is attained by 3 cubes, the smallest of which is 157^3 = 3869893 so that a(7) = 157.
		

Crossrefs

Other powers: A380111, A379650, A380567.

Programs

  • C
    /* See A373727. */
  • Mathematica
    Table[t =SortBy[Map[{#, Total@IntegerDigits[#^3]} &,
        Range[Ceiling@CubeRoot[10^(n - 1)], CubeRoot[10^n - 1]]], Last];
     Select[t, #[[2]] == t[[-1]][[2]] &][[1, 1]], {n, 18}]

Extensions

a(26) and a(35) corrected by Kevin Ryde, Apr 03 2025

A380567 a(n) = k the least number for which k^6 is n digits long and the sum of digits of k^6 is the maximum possible for a 6th power of that length (A373994(n)).

Original entry on oeis.org

1, 2, 3, 4, 6, 7, 12, 16, 23, 46, 64, 96, 143, 202, 277, 461, 547, 977, 1194, 2136, 2896, 3707, 5762, 9763, 13817, 16474, 25847, 43693, 51967, 72539, 121624, 172988, 271427, 463976, 681017, 751204, 1387617, 1732027, 3018897, 3515477, 6765526, 9258023
Offset: 1

Views

Author

Zhining Yang, Jan 26 2025

Keywords

Examples

			a(11) = 64 because among all 11-digit sixth powers (47^6-68^6), 64^6=68719476736 and 68^6=98867482624 have the maximum sum of digits, 96 = A373994(11) and 64 is the least number.
		

Crossrefs

Other powers: A379869, A380111, A379650.

Programs

  • C
    /* See A373994. */
  • Mathematica
    a[n_]:=Module[{s=Ceiling[10^((n-1)/6)],max=0},For[k=s,k<=Floor[(10^n-1)^(1/6)],k++,t=Total@IntegerDigits[k^6];If[t>max,s=k;max=t]];s];Table[a[n],{n,36}]
Showing 1-4 of 4 results.