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 A260734 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 - A002828(k), where A002828(k) = the least number of squares that add up to k. 12
 1, 2, 2, 4, 4, 5, 5, 7, 7, 7, 8, 10, 9, 10, 10, 13, 13, 14, 13, 15, 15, 16, 17, 17, 19, 19, 19, 20, 20, 22, 22, 23, 24, 25, 24, 26, 27, 25, 28, 29, 29, 29, 30, 31, 33, 33, 33, 34, 35, 35, 37, 36, 39, 37, 38, 40, 42, 40, 42, 42, 43, 42, 45, 45, 45, 48, 45, 49, 50, 50, 48, 53, 50, 51, 54, 52, 53, 54, 56, 56, 56, 58, 59, 59, 60, 60, 60, 61, 62, 62, 62, 65, 66, 66, 65 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Antti Karttunen, Table of n, a(n) for n = 1..1024 FORMULA a(n) = A260731(((n+1)^2)-1) - A260731((n^2)-1). [The definition.] Equally, for all n >= 1: a(n) = A260731((n+1)^2) - A260731(n^2). a(n) = A260732(n+1) - A260732(n). a(n) = A260733(n+1) - A260733(n). MATHEMATICA Table[Length[#] - 1 &@ NestWhileList[# - (If[First@ # > 0, 1, Length[ First@ Split@ #] + 1] &@ SquaresR[Range@ 4, #]) &, ((n + 1)^2) - 1, # != (n^2) - 1 &], {n, 95}] (* Michael De Vlieger, Sep 08 2016, after Harvey P. Dale at A002828 *) PROG (Scheme, three variants, the first one utilizing memoization-macro definec) (definec (A260734 n) (let ((end (- (A000290 n) 1))) (let loop ((k (- (A000290 (+ 1 n)) 1)) (s 0)) (if (= k end) s (loop (A255131 k) (+ 1 s)))))) (define (A260734 n) (- (A260731 (A000290 (+ 1 n))) (A260731 (A000290 n)))) (define (A260734 n) (- (A260733 (+ 1 n)) (A260733 n))) CROSSREFS First differences of both A260732 and A260733. Cf. A000290, A002828, A255131. Cf. also A261224. Sequence in context: A152850 A036714 A319398 * A265428 A035644 A288773 Adjacent sequences:  A260731 A260732 A260733 * A260735 A260736 A260737 KEYWORD nonn AUTHOR Antti Karttunen, Aug 12 2015 STATUS approved

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Last modified April 3 20:29 EDT 2020. Contains 333199 sequences. (Running on oeis4.)