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A217833 The largest number not exceeding n^2, such that there are no terms of the sequence in the interval (a(n-1)/2, a(n)/2), with a(0)=0, a(1)=1. 3
0, 1, 2, 4, 8, 16, 32, 49, 64, 81, 98, 121, 128, 162, 196, 225, 242, 256, 324, 361, 392, 441, 450, 484, 512, 625, 648, 722, 784, 841, 882, 900, 968, 1024, 1156, 1225, 1250, 1296, 1444, 1521, 1568, 1681, 1682, 1764, 1800, 1936, 2048, 2209, 2304, 2312, 2450 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Every term has the form s*2^k, where s>=0 is a square and k>=0.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

FORMULA

a(n) = min(2*a(k+1), n^2) for n>=2 and a(k) <= a(n-1)/2 < a(k+1).

EXAMPLE

Let us find a(6), knowing the previous terms. Since a(5) = 16 and a(4)<=16/2<a(5). Then a(6) = 2*a(5) = 32, since 32<6^2 = 36. Further, since a(5)<=a(6)/2<a(6), then a(7) = 7^2 = 49, since 49<2*a(6) = 64.

MAPLE

a:= proc(n) option remember; local i, j, k, t;

      if n<2 then n

    else i, j, k, t:= 0, n-1, iquo(n-1, 2), a(n-1)/2;

         while k<>i do if a(k)<=t then i:=k else j:=k fi;

                       k:= iquo(i+j, 2) od;

         min(n^2, 2*a(k+1))

      fi

    end:

seq (a(n), n=0..100);  # Alois P. Heinz, Nov 03 2012

CROSSREFS

Cf. A217689.

Sequence in context: A323395 A326079 A222193 * A226930 A326751 A297702

Adjacent sequences:  A217830 A217831 A217832 * A217834 A217835 A217836

KEYWORD

nonn

AUTHOR

Vladimir Shevelev, Oct 12 2012

EXTENSIONS

More terms from Alois P. Heinz, Nov 02 2012

STATUS

approved

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Last modified September 18 20:05 EDT 2020. Contains 337173 sequences. (Running on oeis4.)