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

1,3

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.

References

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

Links

Table of n, a(n) for n=1..51.

Example

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.

Mathematica

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

Crossrefs

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

Sequence in context: A160375 A300017 A376023 * A188396 A356090 A190763

Adjacent sequences: A176757 A176758 A176759 * A176761 A176762 A176763

Keyword

base,nonn,changed

Author

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

Extensions

Edited by D. S. McNeil, Nov 21 2010

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

Status

approved