A176974 First exponent n to generate maximum remainder when (a + 1)^n + (a - 1)^n is divided by a^2 for variable n and a>2.
1, 1, 7, 5, 3, 3, 13, 9, 5, 5, 19, 13, 7, 7, 25, 17, 9, 9, 31, 21, 11, 11, 37, 25, 13, 13, 43, 29, 15, 15, 49, 33, 17, 17, 55, 37, 19, 19, 61, 41, 21, 21, 67, 45, 23, 23, 73, 49, 25, 25, 79, 53, 27, 27, 85, 57, 29, 29, 91, 61, 31, 31, 97, 65, 33, 33, 103, 69
Offset: 3
Links
- Colin Barker, Table of n, a(n) for n = 3..1000
- Project Euler, Problem 120: Square remainders
- Index entries for linear recurrences with constant coefficients, signature (0,0,0,2,0,0,0,-1).
Crossrefs
Cf. A159469.
Programs
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PARI
Vec(x^3*(1 + x + 7*x^2 + 5*x^3 + x^4 + x^5 - x^6 - x^7) / ((1 - x)^2*(1 + x)^2*(1 + x^2)^2) + O(x^100)) \\ Colin Barker, Oct 29 2017
Formula
From Colin Barker, Oct 29 2017: (Start)
G.f.: x^3*(1 + x + 7*x^2 + 5*x^3 + x^4 + x^5 - x^6 - x^7) / ((1 - x)^2*(1 + x)^2*(1 + x^2)^2).
a(n) = 2*a(n-4) - a(n-8) for n>10.
(End)
Extensions
Corrected and extended by Ray Chandler, Oct 16 2011