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A236564 Difference between 2^(2n-1) and the nearest square. 3
1, -1, -4, 7, -17, 23, -89, 7, 28, 112, 448, 1792, -4417, 5503, 22012, -4633, -18532, -74128, -296512, 296863, 1187452, -1181833, -4727332, 4817239, 19268956, -17830441, -71321764, 94338007, 377352028, -9092137, -36368548, -145474192, -581896768, -2327587072, -9310348288 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

The distances of the even powers 2^(2n) to their nearest squares are obviously all zero and therefore skipped.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..500

FORMULA

If A201125(n) < A238454(n), a(n) = A201125(n), otherwise a(n) = -A238454(n). [Negative terms are for cases where the nearest square is above 2^(2n-1), not below it.] - Antti Karttunen, Feb 27 2014

EXAMPLE

a(1) = 2^1 - 1^2 = 1.

a(2) = 2^3 - 3^2 = -1.

a(3) = 2^5 - 6^2 = 32 - 36 = -4.

MAPLE

A236564 := proc(n)

    local x, sq, lo, hi ;

    x := 2^(2*n-1) ;

    sq := isqrt(x) ;

    lo := sq^2 ;

    hi := (sq+1)^2 ;

    if abs(x-lo) < abs(x-hi) then

        x-lo ;

    else

        x-hi ;

    end if;

end proc: # R. J. Mathar, Mar 13 2014

MATHEMATICA

Table[2^n - Round[Sqrt[2^n]]^2, {n, 1, 79, 2}] (* Alonso del Arte, Feb 23 2014 *)

PROG

(Python)

def isqrt(a):

    sr = 1 << (int.bit_length(int(a)) >> 1)

    while a < sr*sr:  sr>>=1

    b = sr>>1

    while b:

        s = sr + b

        if a >= s*s:  sr = s

        b>>=1

    return sr

for n in range(47):

    nn = 2**(2*n+1)

    a = isqrt(nn)

    d1 = nn - a*a

    d2 = (a+1)**2 - nn

    if d2 < d1:  d1 = -d2

    print(str(d1), end=', ')

CROSSREFS

Cf. A053188, A201125, A238454.

Sequence in context: A124402 A216552 A034736 * A302549 A023860 A009881

Adjacent sequences:  A236561 A236562 A236563 * A236565 A236566 A236567

KEYWORD

sign,easy

AUTHOR

Alex Ratushnyak, Feb 23 2014

STATUS

approved

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Last modified August 5 07:37 EDT 2021. Contains 346464 sequences. (Running on oeis4.)