A261223 a(n) = number of steps to reach 0 when starting from k = (n*n)-1 and repeatedly applying the map that replaces k with k - A053610(k), where A053610(k) = the number of positive squares that sum to k using the greedy algorithm.

0, 1, 3, 5, 8, 11, 14, 18, 23, 28, 34, 40, 47, 54, 61, 69, 77, 86, 96, 106, 117, 128, 140, 152, 164, 177, 190, 204, 218, 233, 248, 264, 281, 298, 316, 334, 353, 372, 391, 411, 432, 453, 474, 496, 518, 541, 564, 588, 612, 637, 663, 689, 716, 743, 771, 799, 827, 856, 886, 916, 947, 978, 1009, 1041, 1073, 1106, 1139, 1173, 1207, 1242, 1277, 1313, 1350, 1387, 1425, 1463, 1502, 1541

Offset: 1

Author

Antti Karttunen, Aug 12 2015

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..6000

Crossrefs

One less than A261222.

Cf. A053610, A260740, A261221, A261224.

Cf. also A260733, A261228.

Programs

Mathematica

Table[-2 + Length@ NestWhileList[# - Block[{m = #, c = 1}, While[a = (# - Floor[Sqrt@ #]^2) &@ m; a != 0, c++; m = a]; c] &, (n + 1)^2, # != 0 &], {n, 0, 77}] (* Michael De Vlieger, Sep 08 2016, after Jud McCranie at A053610 *)

Formula

a(n) = A261221((n^2)-1).

a(n) = A261222(n)-1.