login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A140716 Blocky integers, i.e., integers n > 1 such that there is a run of n consecutive integer squares the average of which is a square. 0
7, 25, 31, 49, 55, 73, 79, 97, 103, 121, 127, 145, 151, 169, 175, 193, 199, 217, 223, 241, 247, 265, 271, 289, 295, 313, 319, 337, 343, 361, 367, 385, 391, 409, 415, 433, 439, 457, 463, 481, 487, 505, 511, 529, 535, 553, 559, 577, 583 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

For a blocky n, a starting k^2 in the required run of squares is obtained by taking k = a - b - (n-1)/2, where ab = (n^2 - 1)/48.

From Artur Jasinski, Oct 30 2008: (Start)

Numbers congruent to 1 or 7 mod 8.

Positive integers k such that hypergeometric([k/8, (8-k)/8], [1/2], 3/4) = 2cos(Pi/4).(End)

LINKS

Table of n, a(n) for n=1..49.

S. Marivani and others, Problem 11227: Consecutive Squares with a Square Average, Amer. Math. Monthly, 115, No. 6, 2008, 568-569.

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

FORMULA

n is blocky if and only if n>1 and n (mod 24) = 1 or -1 or 7 or -7.

a(n) = 8*(s-1)+1 for n odd, a(n) = 8*(s-1)+7 for n even. - Artur Jasinski, Oct 30 2008

From R. J. Mathar, Nov 25 2008: (Start)

G.f.: x*(7+18*x-x^2)/((1+x)*(1-x)^2).

a(n)= a(n-2) + 24 = 12n - 2 + 3*(-1)^n. (End)

a(n) = a(n-1) + a(n-2) - a(n-3). - Colin Barker, May 12 2012

EXAMPLE

7 is blocky because ((-3)^2 + (-2)^2 + (-1)^2 + 0^2 + 1^2 + 2^2 + 3^2)/7 = 28/7 = 4 = 2^2.

MAPLE

a:=proc(n) if `mod`(n, 24)=1 or `mod`(n, 24)=-1 or `mod`(n, 24)=7 or `mod`(n, 24) =-7 then n else end if end proc: seq(a(n), n=2..600);

MATHEMATICA

Table[12*n - 2 + 3*(-1)^n, {n, 1, 50}] (* Vaclav Kotesovec, Nov 14 2017 *)

CROSSREFS

Cf. A146502-A146522. - Artur Jasinski, Oct 30 2008

Sequence in context: A065660 A100496 A110081 * A141393 A226366 A294459

Adjacent sequences:  A140713 A140714 A140715 * A140717 A140718 A140719

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, Jun 04 2008

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 August 9 05:12 EDT 2020. Contains 336319 sequences. (Running on oeis4.)