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A218721 a(n) = (18^n-1)/17. 35
0, 1, 19, 343, 6175, 111151, 2000719, 36012943, 648232975, 11668193551, 210027483919, 3780494710543, 68048904789775, 1224880286215951, 22047845151887119, 396861212733968143, 7143501829211426575, 128583032925805678351 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Partial sums of powers of 18 (A001027), q-integers for q=18: diagonal k=1 in triangle A022182.
Partial sums are in A014901. Also, the sequence is related to A014935 by A014935(n) = n*a(n) - Sum_{i=0..n-1} a(i), for n>0. - Bruno Berselli, Nov 06 2012
From Bernard Schott, May 06 2017: (Start)
Except for 0, 1 and 19, all terms are Brazilian repunits numbers in base 18, and so belong to A125134. From n = 3 to n = 8286, all terms are composite. See link "Generalized repunit primes".
As explained in the extensions of A128164, a(25667) = (18^25667 - 1)/17 would be (is) the smallest prime in base 18. (End)
LINKS
Harvey Dubner, Generalized repunit primes, Math. Comp., 61 (1993), 927-930.
FORMULA
a(n) = floor(18^n/17).
G.f.: x/((1-x)*(1-18*x)). - Bruno Berselli, Nov 06 2012
a(n) = 19*a(n-1) - 18*a(n-2). - Vincenzo Librandi, Nov 07 2012
E.g.f.: exp(x)*(exp(17*x) - 1)/17. - Stefano Spezia, Mar 11 2023
EXAMPLE
a(3) = (18^3 - 1)/17 = 343 = 7 * 49; a(6) = (18^6 - 1)/17 = 2000719 = 931 * 2149. - Bernard Schott, May 01 2017
MATHEMATICA
LinearRecurrence[{19, -18}, {0, 1}, 40] (* Vincenzo Librandi, Nov 07 2012 *)
Join[{0}, Accumulate[18^Range[0, 20]]] (* Harvey P. Dale, Nov 08 2012 *)
PROG
(PARI) A218721(n)=18^n\17
(Maxima) A218721(n):=(18^n-1)/17$ makelist(A218721(n), n, 0, 30); /* Martin Ettl, Nov 05 2012 */
(Magma) [n le 2 select n-1 else 19*Self(n-1)-18*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Nov 07 2012
CROSSREFS
Sequence in context: A170652 A170700 A170738 * A282030 A192568 A171324
KEYWORD
nonn,easy
AUTHOR
M. F. Hasler, Nov 04 2012
STATUS
approved

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Last modified April 25 10:34 EDT 2024. Contains 371967 sequences. (Running on oeis4.)