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

1,3

Links

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

Formula

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

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

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 *)

Prog

(Scheme, two variants, the other one utilizing memoization-macro definec)
(definec (A260733 n) (if (= 1 n) 0 (+ (A260734 (- n 1)) (A260733 (- n 1)))))
(define (A260733 n) (A260731 (- (* n n) 1)))

Crossrefs

One less than A260732.

Cf. A002828, A255131, A260731, A260734.

Cf. also A261223.

Sequence in context: A152737 A032635 A036713 * A265429 A356254 A122248

Adjacent sequences: A260730 A260731 A260732 * A260734 A260735 A260736

Keyword

nonn

Author

Antti Karttunen, Aug 12 2015

Status

approved