A269447 The first of 23 consecutive positive integers the sum of the squares of which is a square.

7, 17, 881, 1351, 42787, 65337, 2053401, 3135331, 98520967, 150431057, 4726953521, 7217555911, 226795248547, 346292253177, 10881444977241, 16614810597091, 522082563659527, 797164616407697, 25049081610680561, 38247286776972871, 1201833834749007907

Offset: 1

Author

Colin Barker, Feb 27 2016

Keywords

• nonn
• easy

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

Examples

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

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).

Crossrefs

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

Programs

Mathematica

LinearRecurrence[{1,48,-48,-1,1},{7,17,881,1351,42787},30] (* Harvey P. Dale, May 21 2024 *)

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))

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