A260733 a(n) = number of steps needed to reach zero when starting from k = (n^2)-1 and repeatedly applying the map that replaces k with k - A002828(k), where A002828(k) = the least number of squares that add up to k.

0, 1, 3, 5, 9, 13, 18, 23, 30, 37, 44, 52, 62, 71, 81, 91, 104, 117, 131, 144, 159, 174, 190, 207, 224, 243, 262, 281, 301, 321, 343, 365, 388, 412, 437, 461, 487, 514, 539, 567, 596, 625, 654, 684, 715, 748, 781, 814, 848, 883, 918, 955, 991, 1030, 1067, 1105, 1145, 1187, 1227, 1269, 1311, 1354, 1396, 1441, 1486, 1531, 1579, 1624, 1673, 1723, 1773, 1821

Offset: 1

Author

Antti Karttunen, Aug 12 2015

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..1024

Crossrefs

One less than A260732.

Cf. A002828, A255131, A260731, A260734.

Cf. also A261223.

Programs

Mathematica

Table[Length[#] - 2 &@ NestWhileList[# - (If[First@ # > 0, 1, Length[ First@ Split@ #] + 1] &@ SquaresR[Range@ 4, #]) &, n^2, # != 0 &], {n, 72}] (* Michael De Vlieger, Sep 08 2016 *)

Formula

a(n) = A260731((n^2)-1).

a(n) = A260732(n)-1.