login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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