A053700 a(n) = 111111 in base n.
6, 63, 364, 1365, 3906, 9331, 19608, 37449, 66430, 111111, 177156, 271453, 402234, 579195, 813616, 1118481, 1508598, 2000719, 2613660, 3368421, 4288306, 5399043, 6728904, 8308825, 10172526, 12356631, 14900788, 17847789, 21243690, 25137931
Offset: 1
Examples
a(3)=364 because 111111 base 3 = 243 + 81 + 27 + 9 + 3 + 1 = 121.
Links
- Carlos M. da Fonseca and Anthony G. Shannon, A formal operator involving Fermatian numbers, Notes Num. Theor. Disc. Math. (2024) Vol. 30, No. 3, 491-498.
- Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
Programs
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Mathematica
Table[(n^5+n^4+n^3+n^2+n+1),{n,0,5!}] (* Vladimir Joseph Stephan Orlovsky, Mar 06 2010 *) -
PARI
a(n)=(n^6-1)/(n-1) \\ Charles R Greathouse IV, Sep 28 2015
Formula
a(n) = n^5 + n^4 + n^3 + n^2 + n + 1 = (n^6-1)/(n-1).
G.f.: x*(6 + 27*x + 76*x^2 + 6*x^3 + 6*x^4 - x^5)/(1-x)^6. - Colin Barker, May 08 2012
E.g.f.: exp(x)*(1 + 5*x + 26*x^2 + 32*x^3 + 11*x^4+ x^5) - 1. - Stefano Spezia, Oct 03 2024