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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
OFFSET
1,2
LINKS
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. also A261224.
Sequence in context: A152850 A036714 A319398 * A265428 A035644 A288773
KEYWORD
nonn
AUTHOR
Antti Karttunen, Aug 12 2015
STATUS
approved