A053716 a(n) = 1111111 in base n.

7, 127, 1093, 5461, 19531, 55987, 137257, 299593, 597871, 1111111, 1948717, 3257437, 5229043, 8108731, 12204241, 17895697, 25646167, 36012943, 49659541, 67368421, 90054427, 118778947, 154764793, 199411801, 254313151, 321272407, 402321277, 499738093

Offset: 1

Author

Henry Bottomley, Mar 23 2000

Keywords

• nonn
• base
• easy

Comments

Evaluation of the seventh cyclotomic polynomial at n. - Joerg Arndt, Aug 27 2015

Examples

			a(3)=1093 because 1111111 base 3=729+243+81+27+9+3+1=121.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• 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 to values of cyclotomic polynomials of integer argument
• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Crossrefs

7th row of the array A055129.

Cf. A104878.

Programs

Magma

[7] cat [(n^7-1)/(n-1): n in [2..35]]; // Vincenzo Librandi, Feb 08 2014

Maple

A053716 := proc(n)
    numtheory[cyclotomic](7,n) ;
end proc:
seq(A053716(n),n=1..20) ; # R. J. Mathar, Feb 07 2014

Mathematica

Table[FromDigits["1111111",n],{n,1,30}](*or*)Table[n^6+n^5+n^4+n^3+n^2+n+1,{n,1,60}] (* Vladimir Joseph Stephan Orlovsky, Jan 29 2012 *)
CoefficientList[Series[-(x^6 - 6 x^5 + 57 x^4 + 232 x^3 + 351 x^2 + 78 x + 7)/(x - 1)^7, {x, 0, 40}], x] (* Vincenzo Librandi, Feb 08 2014 *)

Formula

a(n) = n^6+n^5+n^4+n^3+n^2+n+1 = (n^7-1)/(n-1).

G.f.: -x*(x^6-6*x^5+57*x^4+232*x^3+351*x^2+78*x+7)/(x-1)^7. - Colin Barker, Oct 29 2012

E.g.f.: exp(x)*(1 + 6*x + 57*x^2 + 122*x^3 + 76*x^4+ 16*x^5 + x^6) - 1. - Stefano Spezia, Oct 03 2024