

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
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OFFSET

1,1


COMMENTS

Positive integers y in the solutions to 2*x^246*y^21012*y7590 = 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(np)  x(n2p) + 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(n1)+48*a(n2)48*a(n3)a(n4)+a(n5) for n>5.
G.f.: x*(7+10*x+528*x^210*x^329*x^4) / ((1x)*(148*x^2+x^4)).
a(1)=7, a(2)=17, a(3)=881, a(4)=1351, a(n) = 48*a(n2)a(n4)+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^210*x^329*x^4)/((1x)*(148*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



