The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A233420 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A233420

Minimal number of c-squares (A020330) and/or 1's which add to n.
(history; published version)

#14 by T. D. Noe at Mon Dec 16 00:14:01 EST 2013

STATUS

editing

approved

#13 by T. D. Noe at Mon Dec 16 00:13:56 EST 2013

NAME

Minimal number of "c-squares" (A020330) and/or 1's which add to n.

STATUS

proposed

editing

#12 by Vladimir Shevelev at Wed Dec 11 06:36:48 EST 2013

STATUS

editing

proposed

#11 by Vladimir Shevelev at Wed Dec 11 06:36:24 EST 2013

DATA

1, 2, 1, 2, 3, 2, 3, 4, 3, 1, 2, 3, 2, 3, 1, 2, 3, 2, 3, 2, 3, 4, 3, 4, 2, 3, 4, 3, 4, 2, 3, 4, 3, 4, 3, 1, 2, 3, 2, 3, 4, 3, 4, 5, 1, 2, 3, 2, 3, 4, 2, 3, 4, 1, 2, 3, 2, 3, 4, 2, 3, 4, 1, 2, 3, 2, 3, 4, 2, 3, 4, 2, 2, 3, 3, 3, 4, 2, 3, 4, 2, 3, 3, 3

STATUS

proposed

editing

#10 by Charles R Greathouse IV at Tue Dec 10 13:57:49 EST 2013

STATUS

editing

proposed

#9 by Charles R Greathouse IV at Tue Dec 10 13:57:41 EST 2013

PROG

(PARI) v=vector(10^5, n, n+n<<#binary(n)); \\ choose large enough that v[#v] > n for a(n) below.

a(n)=if(setsearch(v, n), return(1)); if(n<3, return(n)); my(where=setsearch(v, n+1, 1), t=n); if(!where, where=setsearch(v, n, 1)); forstep(i=where-1, 1, -1, t=min(w(n-v[i]), t); if(t==1, return(2))); t+1 \\ Charles R Greathouse IV, Dec 10 2013

STATUS

proposed

editing

#8 by Vladimir Shevelev at Tue Dec 10 10:14:13 EST 2013

STATUS

editing

proposed

#7 by Vladimir Shevelev at Tue Dec 10 10:11:13 EST 2013

NAME

Smallest Minimal number of numbers in union of {1} and "c-squares" (A020330) the sum of and/or 1's which is add to n.

COMMENTS

Conjecture: the sequence is bounded by a constant.

STATUS

proposed

editing

Discussion

Tue Dec 10

10:14

Vladimir Shevelev: Thank you, Antti, you are right, I corrected name and comment.

#6 by Vladimir Shevelev at Mon Dec 09 14:20:52 EST 2013

STATUS

editing

proposed

Discussion

Mon Dec 09

17:05

Antti Karttunen: The name is slightly cumbersome. I suggest something like:
Minimal number of  "c-squares" (A020330) and/or unities which add to n.
(Or maybe just 1's instead of "unities".)
BTW, why the sequence should be bounded (I assume you mean: by some constant?)

17:13

Antti Karttunen: Look at those discontinuities: https://oeis.org/A020330/graph
they are getting exponentially larger.
From
https://oeis.org/A020330/b020330.txt
we have A020330(255)=65535 and A020330(256)=131328.
32896 - 16383 = 16513 and 16513 - 16383 = 130.
Just a lot's of hand waving, but...

#5 by Vladimir Shevelev at Mon Dec 09 14:20:46 EST 2013

NAME

Smallest number of numbers in union of {1} and "c-squares" (A020330) the sum of which is n.

STATUS

proposed

editing