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

0,5

Links

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

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)

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 *)

Prog

(Scheme, with memoization-macro definec)
(definec (A260731 n) (if (zero? n) n (+ 1 (A260731 (A255131 n)))))

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.

Sequence in context: A085003 A119026 A064775 * A194239 A064475 A025774

Adjacent sequences: A260728 A260729 A260730 * A260732 A260733 A260734

Keyword

nonn

Author

Antti Karttunen, Aug 12 2015

Status

approved