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 1-7 of 7 results.

A055565 Sum of digits of n^4.

Original entry on oeis.org

0, 1, 7, 9, 13, 13, 18, 7, 19, 18, 1, 16, 18, 22, 22, 18, 25, 19, 27, 10, 7, 27, 22, 31, 27, 25, 37, 18, 28, 25, 9, 22, 31, 27, 25, 19, 36, 28, 25, 18, 13, 31, 27, 25, 37, 18, 37, 43, 27, 31, 13, 27, 25, 37, 27, 28, 43, 18, 31, 22, 18, 34, 37, 36, 37, 34, 45, 13, 31, 27, 7
Offset: 0

Views

Author

Henry Bottomley, Jun 19 2000

Keywords

Examples

			a(2) = 7 because 2^4 = 16 and 1+6 = 7.
		

Crossrefs

Cf. A000583, A007953, A055570, A055575 (fixed points), A373914.

Programs

  • Maple
    for i from 0 to 200 do printf(`%d,`,add(j, j=convert(i^4, base, 10))) od;
  • Mathematica
    a[n_Integer]:=Apply[Plus, IntegerDigits[n^4]]; Table[a[n], {n, 0, 100}] (* Vincenzo Librandi, Feb 23 2015 *)
  • PARI
    a(n) = sumdigits(n^4); \\ Seiichi Manyama, Nov 16 2021
  • Sage
    [sum((n^4).digits()) for n in (0..70)] # Bruno Berselli, Feb 23 2015
    

Formula

a(n) = A007953(A000583(n)). - Michel Marcus, Feb 23 2015

Extensions

More terms from James Sellers, Jul 04 2000

A055575 Sum of digits of n^4 is equal to n.

Original entry on oeis.org

0, 1, 7, 22, 25, 28, 36
Offset: 1

Views

Author

Henry Bottomley, May 26 2000

Keywords

Examples

			7 is a member because 7^4 = 2401 and 2+4+0+1 = 7.
		

Crossrefs

Programs

  • Magma
    [n: n in [0..50] | &+Intseq(n^4) eq n ]; // Vincenzo Librandi, Feb 23 2015
    
  • Mathematica
    Select[Range[0, 50], #==Total[IntegerDigits[#^4]] &] (* Vincenzo Librandi, Feb 23 2015 *)
  • PARI
    isok(k)=sumdigits(k^4)==k \\ Patrick De Geest, Dec 10 2024
  • Sage
    [n for n in (0..50) if sum((n^4).digits()) == n] # Bruno Berselli, Feb 23 2015
    

A055571 Sum of digits of a(n)^5 is greater than or equal to a(n).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 22, 23, 24, 25, 26, 27, 28, 31, 33, 35, 36, 37, 38, 46
Offset: 1

Views

Author

Henry Bottomley, May 26 2000

Keywords

Examples

			a(2) = 2 because 2^5 = 32 and 3+2 = 5>= 2
		

Crossrefs

Programs

  • Mathematica
    Select[Range[0,50],Total[IntegerDigits[#^5]]>=#&] (* Harvey P. Dale, Jul 03 2021 *)

A055572 Sum of digits of a(n)^6 is greater than or equal to a(n).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 39, 42, 44, 45, 46, 51, 52, 54, 64
Offset: 0

Views

Author

Henry Bottomley, May 26 2000

Keywords

Examples

			a(2) = 2 because 2^6 = 64 and 6+4 = 10>= 2
		

Crossrefs

A055569 Sum of digits of a(n)^3 is greater than or equal to a(n).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 15, 16, 17, 18, 19, 26, 27
Offset: 0

Views

Author

Henry Bottomley, May 26 2000

Keywords

Examples

			a(4) = 4 because 4^3 = 64 and 6+4 = 10>= 4
		

Crossrefs

Programs

  • Mathematica
    Select[Range[300],Total[IntegerDigits[#^3]]>=#&] (* Harvey P. Dale, Aug 27 2013 *)

A055568 Numbers not greater than the sum of digits of their squares.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 13, 14, 17
Offset: 1

Views

Author

Henry Bottomley, May 26 2000

Keywords

Examples

			4 is a term because 4^2 = 16 and 1+6 = 7 >= 4.
		

Crossrefs

A081030 a(n) = largest k such that (sum of digits of k^n) >= k.

Original entry on oeis.org

9, 17, 27, 36, 46, 64, 68, 74, 88, 117, 123, 138, 146, 154, 199, 204, 216, 232, 232, 242, 259, 256, 284, 323, 337, 344, 341, 357, 358, 396, 443, 393, 423, 465, 477, 484, 519, 521, 533, 518, 569, 597, 591, 626, 638, 682, 666, 667, 695, 712, 698, 739, 746, 784
Offset: 1

Views

Author

David W. Wilson, Mar 02 2003

Keywords

Examples

			a(2) = 17. We have 17^2 = 289 and 2+8+9 >= 17. No number > 17 has this property.
		

Crossrefs

Programs

  • Mathematica
    (* the constant 20 may need to be higher for larger n *) Table[Select[Range[20*n], Total[IntegerDigits[#^n]] >= # &][[-1]], {n, 100}] (* T. D. Noe, Oct 21 2011 *)

Extensions

Definition corrected by Harvey P. Dale, Oct 21 2011
Showing 1-7 of 7 results.