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A138858 a(n)=least square such that the subsets of {a(1),...,a(n)} sum to 2^n different values. 2
1, 4, 9, 16, 36, 81, 144, 324, 625, 1156, 2401, 4900, 9801, 19600, 39204, 78400, 156816, 313600, 627264, 1254400, 2509056, 5022081, 10042561, 20088324, 40182921, 80371225, 160731684, 321484900, 642977449, 1285939600 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Asking for 2^n different values implies that a(n) differs from all a(k), k<n and in view of the minimality condition, also that a(n) > a(n-1) for n>1.

Note that a(n) is close to, but not always larger than sum(a(k),k=1..n-1), as opposed to the case in A064934.

LINKS

Table of n, a(n) for n=1..30.

EXAMPLE

Up to a(4)=16, we have a(n)=n^2.

But since 5^2=25=9+16 is already represented as sum of earlier terms, this is excluded, while a(5)=6^2=36 has the required property.

Obviously, any square larger to the sum of all preceding terms leads to enough new terms, thus a(n) <= floor( sqrt( sum(a(k),k=1..n-1))+1)^2.

But in contrast to A064934, such a simple formula (with equality) cannot be used here:

a(7)=12^2=144 < 147=sum(a(k),k<7) and also a(10)=sum(a(k),k<10)-84.

PROG

(PARI) {s=1; p=0; for( n=1, 20, until( !bitand( s, s>>(p^2) ), p++); s+=s<<(p^2); print1( p^2, ", "))}

CROSSREFS

Cf. A138857 (=sqrt(a(n))), A138000-138001, A064934.

Sequence in context: A272711 A018228 A204503 * A076967 A233247 A231180

Adjacent sequences:  A138855 A138856 A138857 * A138859 A138860 A138861

KEYWORD

nonn

AUTHOR

M. F. Hasler, Apr 09 2008

EXTENSIONS

a(24)-a(30) from Donovan Johnson, Oct 03 2009

STATUS

approved

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Last modified October 22 22:34 EDT 2019. Contains 328335 sequences. (Running on oeis4.)