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A101412 Least number of odd squares that sum to n. 2
1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 9, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 9, 2, 3, 4, 5, 6, 7, 8, 9, 10, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 9, 2, 3, 4, 5, 6, 7, 8, 9, 10, 3, 4, 5, 6, 7, 8, 9, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 9, 2, 3, 4, 5, 6, 7, 8, 9, 2, 3, 4, 5, 6, 7, 8, 9 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

FORMULA

From Jinyuan Wang, Jan 29 2019: (Start)

For n == 1 (mod 8), if n is a perfect square, a(n) = 1, otherwise a(n) = 9.

For n == 2 (mod 8), if n is a term in A097269, a(n) = 2, otherwise a(n) = 10.

For n == k (mod 8), k = 3,4,...,8, a(n) = k.

For positive integer x, a(72*x+42) = a(72*x+66) = 10. (End)

EXAMPLE

a(13) = 5: 13 = 1+1+1+1+9.

MAPLE

A101412 := proc(n) local lsq; lsq := [seq((2*j+1)^2, j=0..floor((sqrt(n)-1)/2))] ; lsq := convert(lsq, set) ; a := n ; for p in combinat[partition](n) do if convert(p, set) minus lsq = {} then a := min(a, nops(p)) ; fi; od: a ; end: for n from 1 do printf("%d, \n", A101412(n)) ; od: # R. J. Mathar, Aug 08 2009

# problem has optimal substructure:

a:= proc(n) option remember; local r; r:= isqrt(n);

      `if`(r^2=n and irem(r, 2)=1, 1,

       min(seq(a(i)+a(n-i), i=1..n/2)))

    end:

seq(a(n), n=1..120);  # Alois P. Heinz, Jan 31 2011

MATHEMATICA

a[n_] := a[n] = Module[{r}, r = Sqrt[n]; If[IntegerQ[r] && OddQ[r], 1, Min[Table[a[i]+a[n-i], {i, 1, Floor[n/2]}]]]]; Table[a[n], {n, 1, 105}] (* Jean-Fran├žois Alcover, Mar 19 2014, after Alois P. Heinz *)

PROG

(PARI) a(n)={x=n-1; if(x%8>1, k=1+x%8); if(n%8==1, k=9; if(issquare(n)&&n%2==1, k=1)); if(x%8==1, k=10; y=1; while(x>0, if(issquare(x)&&x%2==1, k=2); y=y+2; x=n-y^2)); k; } \\ Jinyuan Wang, Jan 29 2019

CROSSREFS

Cf. A002828, A151925, A097269.

Sequence in context: A190598 A053844 A010887 * A053830 A033929 A025482

Adjacent sequences:  A101409 A101410 A101411 * A101413 A101414 A101415

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Aug 08 2009

EXTENSIONS

More terms from R. J. Mathar, Aug 08 2009

More terms from Alois P. Heinz, Jan 30 2011

STATUS

approved

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Last modified February 27 19:23 EST 2020. Contains 332308 sequences. (Running on oeis4.)