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Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!) A053716 a(n) = 1111111 in base n. 18 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 (list; graph; refs; listen; history; text; internal format) 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 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] 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 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

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Last modified April 26 09:05 EDT 2024. Contains 371991 sequences. (Running on oeis4.)