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A269447 The first of 23 consecutive positive integers the sum of the squares of which is a square. 5
7, 17, 881, 1351, 42787, 65337, 2053401, 3135331, 98520967, 150431057, 4726953521, 7217555911, 226795248547, 346292253177, 10881444977241, 16614810597091, 522082563659527, 797164616407697, 25049081610680561, 38247286776972871, 1201833834749007907 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Positive integers y in the solutions to 2*x^2-46*y^2-1012*y-7590 = 0.

All sequences of this type (i.e. sequences with fixed offset k, and a discernible pattern: k=0...22 for this sequence, k=0..1 for A001652, k=0...10 for A106521) can be continued using a formula such as x(n) = a*x(n-p) - x(n-2p) + b, where a and b are various constants, and p is the period of the series. Alternatively 'p' can be considered the number of concurrent series. - Daniel Mondot, Aug 05 2016

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,48,-48,-1,1).

FORMULA

a(n) = a(n-1)+48*a(n-2)-48*a(n-3)-a(n-4)+a(n-5) for n>5.

G.f.: x*(7+10*x+528*x^2-10*x^3-29*x^4) / ((1-x)*(1-48*x^2+x^4)).

a(1)=7, a(2)=17, a(3)=881, a(4)=1351, a(n) = 48*a(n-2)-a(n-4)+506. - Daniel Mondot, Aug 05 2016

EXAMPLE

7 is in the sequence because sum(k=7, 29, k^2) = 8464 = 92^2.

PROG

(PARI) Vec(x*(7+10*x+528*x^2-10*x^3-29*x^4)/((1-x)*(1-48*x^2+x^4)) + O(x^30))

CROSSREFS

Cf. A001032, A001652, A094196, A106521, A257761, A269448, A269449, A269451.

Sequence in context: A159028 A102266 A113765 * A013540 A153375 A001145

Adjacent sequences:  A269444 A269445 A269446 * A269448 A269449 A269450

KEYWORD

nonn,easy

AUTHOR

Colin Barker, Feb 27 2016

STATUS

approved

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Last modified October 23 22:04 EDT 2018. Contains 316541 sequences. (Running on oeis4.)