[seqfan] A099107

[Don Reble]

> %I A099107
> %S 2,3,5,8,10,11,14,18,20,21,24,26,28,32,34,36,38,40,42
> %N Larger value of the smallest set of integer numbers where no pair
>    of consecutive numbers sums to a square.
> %C Other unique solutions:
> %C (14,28) 2 4 6 9 11 13 15 17 18 20 22 24 26 28
> %C (16,34) 3 5 8 10 12 14 16 18 19 21 23 25 27 29 32 34
> %C (17,36) 3 5 8 10 12 14 16 18 19 21 23 25 27 29 32 34 36
> %C (18,38) 3 5 8 10 12 14 16 18 19 21 23 25 27 29 32 34 36 38
> %C (19,40) 3 5 8 10 12 14 16 18 19 21 23 25 27 29 32 34 36 38 40
> %C (20,42) 3 5 8 10 12 14 16 18 19 21 23 25 27 29 32 34 36 38 40 42
> %K nonn,obsc
> %O 2,1
> %A Jean-Charles Meyrignac (euler(AT)free.fr), Nov 14 2004


> The definition seems unclear to me. - njas, Nov 17 2004

    I think the definition should be

        a(n) is the least M such that there are n values in 1..M,
        with no two values summing to a square.

    Those six "unique solutions" tend to confirm. The (14,28) sequence
    is indeed the unique subset of 1..28 which has 14 values and no
    square pair-sum. Likewise for the other five. But (15,32) has two
    subsets,
        3 5 8 10 12 14 16 18 19 21 23 25 27 29 32
        3 5 8 10 12 14 16 18 21 23 25 27 29 30 32
    so it's not listed.

    But my version (starting at n=1) differs slightly:

        1,2,4,6,9,10,11,15,18,20,21,24,26,28,32,34,36,38,40,42
(J-C M)   2,3,5,8,10,11,14,18,20,21,24,26,28,32,34,36,38,40,42
            - -         --

    More terms:

%S A099107 1,2,4,6,9,10,11,15,18,20,21,24,26,28,32,34,36,38,40,42,50,52,54,56,
%T A099107 58,60,62,64,72,74,76,78,80
%O A099107 1,2

-- 
Don Reble  djr at nk.ca


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