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 1-5 of 5 results.

A373914 a(n) is the largest digit sum of all n-digit fourth powers.

Original entry on oeis.org

1, 9, 13, 19, 25, 37, 43, 52, 55, 70, 76, 79, 85, 99, 103, 108, 118, 127, 135, 142, 144, 153, 171, 166, 178, 181, 189, 198, 205, 211, 220, 232, 234, 243, 252, 261, 265, 274, 279, 283, 297, 298, 313, 316, 325, 334, 337, 346, 358
Offset: 1

Views

Author

Zhining Yang, Jun 22 2024

Keywords

Examples

			a(3) = 13 because 13 is the largest digital sum encountered among all 3-digit fourth powers (attained at both fourth powers: 256, 625).

Links

Crossrefs

Cf. A055565, A018072, A018074, A380111, A380797.
Other powers: A371728, A373727, A374025, A373994.

Programs

  • C
    /* See links. */
  • Mathematica
    Table[Max@Map[Total@IntegerDigits[#^4] &, Range[Ceiling[10^((n - 1)/4)], Floor[(10^n-1)^(1/4)]]], {n, 32}]
  • PARI
    a(n) = my(m=ceil(10^((n-1)/4)), M=sqrtint(sqrtint(10^n))); vecmax(apply(sumdigits, vector(M-m+1, i, (i+m-1)^4))); \\ Michel Marcus, Jun 23 2024
  • Python
    from sympy import integer_nthroot
def A373914(n): return max(sum(int(d) for d in str(m**4)) for m in range((lambda x:x[0]+(x[1]^1))(integer_nthroot(10**(n-1),4)),1+integer_nthroot(10**n-1,4)[0])) # Chai Wah Wu, Jun 26 2024

A379650 a(n) is the least number whose fifth power is an n-digit fifth power which has the maximum sum of digits (A374025(n)).

Original entry on oeis.org

1, 2, 3, 6, 9, 15, 18, 37, 58, 93, 156, 179, 368, 549, 756, 1379, 2139, 3965, 4956, 9746, 11156, 25046, 38779, 60006, 98746, 151446, 231755, 389658, 585516, 819199, 1584779, 1776339, 3803469, 5400759, 9744998, 11463799, 23936959, 28737498, 62943519, 95635199, 156373159, 225142779, 351816939, 595519999
Offset: 1

Views

Author

Zhining Yang, Jan 12 2025

Keywords

Examples

			a(7) = 18 because among all 7-digit fifth powers (16^5 to 25^5), 18^5=1889568 is the item which has the maximum sum of digits, 45 = A374025(7).

Links

Crossrefs

Cf. A000584, A374025.
Cf. A370522, A373914, A379869, A380111.

Programs

  • Mathematica
    a[n_]:=Module[{s=Floor[(10^n-1)^(1/5)],max=0},
For[k=s,k>=Ceiling[10^((n-1)/5)],k--,t=DigitSum[k^5];
If[t>max,s=k;max=t]];s];
For[n=1,n<=30,n++,Print[{n,a[n]}]]

A380797 a(n) is the largest number whose fourth power is an n-digit which has the maximum sum of digits (A373914(n)).

Original entry on oeis.org

1, 3, 5, 8, 16, 26, 56, 88, 118, 308, 518, 974, 1768, 2868, 5396, 8979, 17306, 28871, 55368, 97063, 167622, 289146, 562341, 835718, 1727156, 3154276, 5623116, 9397404, 17728256, 27831542, 53129506, 98665756, 166025442, 315265896, 510466356, 904245732, 1188893858, 2298249374, 5315776056
Offset: 1

Views

Author

Zhining Yang, Feb 03 2025

Keywords

Examples

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

Crossrefs

Cf. A373914, A380111.
Other powers: A379298, A380052, A380566, A380193.

Programs

  • C
    /* See A373914. */
  • Mathematica
    a[n_]:=Module[{m=Floor[(10^n-1)^(1/4)], max=0},
For[k=m, k>=Ceiling[10^((n-1)/4)], k--, t=Total@IntegerDigits[k^4];
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

Cf. A373727, A380052.
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.

Links

Crossrefs

Cf. A373994, A380193.
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 1-5 of 5 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.