A176760 Numbers k such that k^2 and k^4 have the same sum of digits.

0, 1, 3, 10, 17, 19, 27, 30, 57, 93, 100, 170, 190, 219, 267, 270, 300, 314, 327, 359, 387, 417, 423, 424, 570, 685, 693, 807, 828, 891, 917, 930, 963, 1000, 1207, 1223, 1317, 1333, 1673, 1693, 1700, 1827, 1864, 1900, 1917, 2141, 2190, 2202, 2213, 2364, 2367

Offset: 1

Author

Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 25 2010

Keywords

• base
• nonn

Comments

Let sod(n) := digital sum of n (A007953); here we have sod(n^2) = sod(n^4).

Trivial cases:

(I) Powers of 10, as sod((10^k)^2) = sod((10^k)^4) = 1.

(II) If N is a term of sequence, then so is 10 * N.

Examples

			sod(3^2) = sod(9) = 9 = sod(81) = sod(3^4), so 3 is a term.
sod(17^2) = sod(289) = 19 = sod(83521) = sod(17^4), so 17 is a term.
		

References

• Hans Schubart, Einfuehrung in die klassische und moderne Zahlentheorie, Vieweg, Braunschweig, 1974.

Crossrefs

Cf. A000290, A000583, A058369, A176012, A176111, A176465.

Programs

Mathematica

Select[Range[0,2000],Total[IntegerDigits[#^2]]==Total[IntegerDigits[#^4]]&]  (* Harvey P. Dale, Jan 19 2011 *)

Extensions

Edited by D. S. McNeil, Nov 21 2010

a(43)-a(51) from Jason Yuen, Oct 13 2024