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

1,3

Links

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

Formula

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

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

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 *)

Prog

(Scheme, two variants, the other one using memoization-macro definec)
(definec (A261223 n) (if (= 1 n) 0 (+ (A261224 (- n 1)) (A261223 (- n 1)))))
(define (A261223 n) (A261221 (- (* n n) 1)))

Crossrefs

One less than A261222.

Cf. A053610, A260740, A261221, A261224.

Cf. also A260733, A261228.

Sequence in context: A005356 A060432 A156023 * A062009 A062484 A348450

Adjacent sequences: A261220 A261221 A261222 * A261224 A261225 A261226

Keyword

nonn

Author

Antti Karttunen, Aug 12 2015

Status

approved