A261222 a(n) = number of steps to reach 0 when starting from k = n*n 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, 2, 4, 6, 9, 12, 15, 19, 24, 29, 35, 41, 48, 55, 62, 70, 78, 87, 97, 107, 118, 129, 141, 153, 165, 178, 191, 205, 219, 234, 249, 265, 282, 299, 317, 335, 354, 373, 392, 412, 433, 454, 475, 497, 519, 542, 565, 589, 613, 638, 664, 690, 717, 744, 772, 800, 828, 857, 887, 917, 948, 979, 1010, 1042, 1074, 1107, 1140, 1174, 1208, 1243, 1278, 1314, 1351, 1388, 1426, 1464, 1503

Offset

0,3

Links

Antti Karttunen, Table of n, a(n) for n = 0..6000

Formula

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

Other identities. For all n >= 1:

a(n) = 1 + A261223(n).

Mathematica

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

Prog

(Scheme, two variants, the other one using memoization-macro definec)
(definec (A261222 n) (if (<= n 1) n (+ (A261224 (- n 1)) (A261222 (- n 1)))))
(define (A261222 n) (A261221 (* n n)))

Crossrefs

Essentially one more than A261223.

First differences: A261224.

Cf. A000290, A053610, A260740, A261221.

Cf. also A260732, A261227.

Sequence in context: A194229 A194201 A194203 * A130025 A278299 A145802

Adjacent sequences: A261219 A261220 A261221 * A261223 A261224 A261225

Keyword

nonn

Author

Antti Karttunen, Aug 12 2015

Status

approved