login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A008319 Smallest number that is sum of squares of distinct earlier terms. 0
1, 1, 2, 4, 5, 6, 16, 17, 18, 20, 21, 22, 25, 26, 27, 29, 30, 31, 36, 37, 38, 40, 41, 42, 43, 45, 46, 47, 52, 53, 54, 56, 57, 58, 61, 62, 63, 65, 66, 67, 77, 78, 79, 81, 82, 83, 256, 257, 258, 260, 261, 262, 272, 273, 274, 276, 277, 278, 281, 282, 283, 285, 286, 287, 289, 290, 291 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Up to a(99999680)=10^8, the largest number not in the sequence is 892. I also computed, up to a(99934078)=10^8, the similar sequence which starts with 1,2 instead of 1,1. The largest number not in that sequence seems to be 134179 - Giovanni Resta, Oct 06 2011

Resta's conjecture is correct. Let x = floor(sqrt(n) - 12). For n > 1935, x^2 > n/2. For n > 1853, n - x^2 > 892. So n > 1935 can be decomposed into x^2 plus a number greater than 892. Since the other number is smaller than x^2, any decomposition into squares will use only numbers smaller than x. By induction, all numbers greater than 1935 (and hence greater than 892) are in this sequence. - Charles R Greathouse IV, Oct 06 2011

REFERENCES

Mihaly Bencze [Beneze], Smarandache Recurrence Type Sequences, Bull. Pure Appl. Sciences, Vol. 16E, No. 2 (1997), pp. 231-236.

LINKS

Table of n, a(n) for n=1..67.

F. Smarandache, Definitions, Solved and Unsolved Problems, Conjectures, ...

F. Smarandache, Sequences of Numbers Involved in Unsolved Problems.

Eric Weisstein's World of Mathematics, Smarandache Sequences

Index entries for linear recurrences with constant coefficients, signature (2,-1).

FORMULA

For n > 572, a(n) = n + 320. - Charles R Greathouse IV, Oct 06 2011

CROSSREFS

Sequence in context: A058637 A026473 A272929 * A033311 A098504 A137653

Adjacent sequences:  A008316 A008317 A008318 * A008320 A008321 A008322

KEYWORD

nonn,easy,nice

AUTHOR

R. Muller

EXTENSIONS

More terms from David W. Wilson

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 December 16 06:18 EST 2019. Contains 330016 sequences. (Running on oeis4.)