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

%I A176760 #19 Oct 13 2024 18:52:06
%S A176760 0,1,3,10,17,19,27,30,57,93,100,170,190,219,267,270,300,314,327,359,
%T A176760 387,417,423,424,570,685,693,807,828,891,917,930,963,1000,1207,1223,
%U A176760 1317,1333,1673,1693,1700,1827,1864,1900,1917,2141,2190,2202,2213,2364,2367
%N A176760 Numbers k such that k^2 and k^4 have the same sum of digits.
%C A176760 Let sod(n) := digital sum of n (A007953); here we have sod(n^2) = sod(n^4).
%C A176760 Trivial cases:
%C A176760 (I) Powers of 10, as sod((10^k)^2) = sod((10^k)^4) = 1.
%C A176760 (II) If N is a term of sequence, then so is 10 * N.
%D A176760 Hans Schubart, Einfuehrung in die klassische und moderne Zahlentheorie, Vieweg, Braunschweig, 1974.
%e A176760 sod(3^2) = sod(9) = 9 = sod(81) = sod(3^4), so 3 is a term.
%e A176760 sod(17^2) = sod(289) = 19 = sod(83521) = sod(17^4), so 17 is a term.
%t A176760 Select[Range[0,2000],Total[IntegerDigits[#^2]]==Total[IntegerDigits[#^4]]&]  (* _Harvey P. Dale_, Jan 19 2011 *)
%Y A176760 Cf. A000290, A000583, A058369, A176012, A176111, A176465.
%K A176760 base,nonn
%O A176760 1,3
%A A176760 Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 25 2010
%E A176760 Edited by _D. S. McNeil_, Nov 21 2010
%E A176760 a(43)-a(51) from _Jason Yuen_, Oct 13 2024