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

1,1

Comments

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

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).

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

Example

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

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 *)

Prog

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

Crossrefs

7th row of the array A055129.

Cf. A104878.

Sequence in context: A139987 A061744 A256146 * A088550 A255954 A278791

Adjacent sequences: A053713 A053714 A053715 * A053717 A053718 A053719

Keyword

nonn,base,easy

Author

Henry Bottomley, Mar 23 2000

Status

approved