|
%I #16 Nov 29 2016 22:38:47
%S 0,1,1,1,2,2,2,2,3,4,4,4,5,5,5,5,6,6,7,7,8,8,8,8,9,10,10,10,10,11,11,
%T 11,12,12,13,13,14,14,14,14,15,15,15,16,16,17,17,17,18,19,19,19,20,20,
%U 20,20,21,21,22,22,22,23,23,23,24,24,24,25,25,25,26,26,27,27,28,28,28,29,29,29,30,31,31,31,32,32,32,32,33,33,34,34,34,35,35,35,36,36,37,37,38
%N a(n) = Number of steps to reach 0 starting from x=n and using the iterated process: x -> x - A002828(x), where A002828(x) = the least number of squares that add up to x.
%H Antti Karttunen, <a href="/A260731/b260731.txt">Table of n, a(n) for n = 0..10000</a>
%F a(0) = 0; for >= 1, a(n) = 1 + A260731(A255131(n)).
%F From _Antti Karttunen_, Nov 28 2016: (Start)
%F For all n >= 0, a(A278517(n)) = a(A278519(n)) = a(A276573(n)) = n.
%F (End)
%t A002828[n_] := Which[n == 0, 0, SquaresR[1, n] > 0, 1, SquaresR[2, n] > 0, 2, SquaresR[3, n] > 0, 3, True, 4]; a[0] = 0; a[n_] := a[n] = 1 + a[n - A002828[n]]; Table[a[n], {n, 0, 100}] (* _Jean-François Alcover_, Nov 14 2016 *)
%o (Scheme, with memoization-macro definec)
%o (definec (A260731 n) (if (zero? n) n (+ 1 (A260731 (A255131 n)))))
%Y Cf. A002828, A255131, A260732, A260733, A260734.
%Y Left inverse of A276573, A278517 and A278519. A278518(n) gives the number of times n occurs (run lengths).
%Y Cf. also A261221.
%K nonn
%O 0,5
%A _Antti Karttunen_, Aug 12 2015
|
