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A176760 Numbers n such that n^2 and n^4 have the same sum of digits. 0
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 (list; graph; refs; listen; history; text; internal format)
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..42.

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]]&]  [From Harvey P. Dale, Jan. 19, 2011]

CROSSREFS

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

Sequence in context: A059911 A160375 A300017 * A188396 A190763 A043405

Adjacent sequences:  A176757 A176758 A176759 * A176761 A176762 A176763

KEYWORD

base,nonn

AUTHOR

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

EXTENSIONS

Edited by D. S. McNeil, Nov 21 2010

STATUS

approved

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Last modified March 24 06:56 EDT 2019. Contains 321444 sequences. (Running on oeis4.)