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 A261224 a(n) = number of steps needed to reach (n^2)-1 when starting from k = ((n+1)^2)-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. 9
 1, 2, 2, 3, 3, 3, 4, 5, 5, 6, 6, 7, 7, 7, 8, 8, 9, 10, 10, 11, 11, 12, 12, 12, 13, 13, 14, 14, 15, 15, 16, 17, 17, 18, 18, 19, 19, 19, 20, 21, 21, 21, 22, 22, 23, 23, 24, 24, 25, 26, 26, 27, 27, 28, 28, 28, 29, 30, 30, 31, 31, 31, 32, 32, 33, 33, 34, 34, 35, 35, 36, 37, 37, 38, 38, 39, 39, 39, 40, 41, 41, 42, 42, 42, 43, 43, 44, 44, 45, 45, 46 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Antti Karttunen, Table of n, a(n) for n = 1..6000 FORMULA a(n) = A261221(((n+1)^2)-1) - A261221((n^2)-1). [The definition.] Equally, for all n >= 1: a(n) = A261221((n+1)^2) - A261221(n^2). a(n) = A261222(n+1) - A261222(n). a(n) = A261223(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 + 1)^2) - 1, # != n^2 - 1 &], {n, 91}] (* Michael De Vlieger, Sep 08 2016, after Jud McCranie at A053610 *) PROG (Scheme, three variants, the first one utilizing memoization-macro definec) (definec (A261224 n) (let ((end (- (A000290 n) 1))) (let loop ((k (- (A000290 (+ 1 n)) 1)) (s 0)) (if (= k end) s (loop (A260740 k) (+ 1 s)))))) (define (A261224 n) (- (A261223 (+ 1 n)) (A261223 n))) (define (A261224 n) (- (A261221 (A000290 (+ 1 n))) (A261221 (A000290 n)))) CROSSREFS First differences of both A261222 and A261223. Cf. A000290, A053610, A260740, A261221. Cf. also A260734, A261229. Sequence in context: A131411 A300068 A194202 * A125059 A029112 A302984 Adjacent sequences:  A261221 A261222 A261223 * A261225 A261226 A261227 KEYWORD nonn AUTHOR Antti Karttunen, Aug 12 2015 STATUS approved

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Last modified June 2 06:39 EDT 2020. Contains 334767 sequences. (Running on oeis4.)