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 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 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

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