

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.


12



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
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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 memoizationmacro 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



