A260731 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.

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, 11, 12, 12, 13, 13, 14, 14, 14, 14, 15, 15, 15, 16, 16, 17, 17, 17, 18, 19, 19, 19, 20, 20, 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

Offset: 0

Author

Antti Karttunen, Aug 12 2015

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A002828, A255131, A260732, A260733, A260734.

Left inverse of A276573, A278517 and A278519. A278518(n) gives the number of times n occurs (run lengths).

Cf. also A261221.

Programs

Mathematica

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 *)

Formula

a(0) = 0; for >= 1, a(n) = 1 + A260731(A255131(n)).

From Antti Karttunen, Nov 28 2016: (Start)

For all n >= 0, a(A278517(n)) = a(A278519(n)) = a(A276573(n)) = n.

(End)