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A264981 Highest power of 9 dividing n. 2
1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 1, 81, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 1, 9 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,9

COMMENTS

The generalized binomial coefficients produced by this sequence provide an analog to Kummer's Theorem using arithmetic in base 9. - Tom Edgar, Feb 02 2016

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..6561

Tyler Ball, Tom Edgar, and Daniel Juda, Dominance Orders, Generalized Binomial Coefficients, and Kummer's Theorem, Mathematics Magazine, Vol. 87, No. 2, April 2014, pp. 135-143.

Tom Edgar and Michael Z. Spivey, Multiplicative functions, generalized binomial coefficients, and generalized Catalan numbers, Journal of Integer Sequences, Vol. 19 (2016), Article 16.1.6.

FORMULA

a(n) = 9^valuation(n,9). - Tom Edgar, Feb 02 2016

G.f.: x/(1 - x) + 8 * Sum_{k>=1} 9^(k-1)*x^(9^k)/(1 - x^(9^k)). - Ilya Gutkovskiy, Jul 10 2019

EXAMPLE

Since 18 = 9 * 2, a(18) = 9. Likewise, since 9 does not divide 17, a(17) = 1. - Tom Edgar, Feb 02 2016

MATHEMATICA

Table[9^Length@ TakeWhile[Reverse@ IntegerDigits[n, 9], # == 0 &], {n, 99}] (* Michael De Vlieger, Dec 09 2015 *)

9^Table[IntegerExponent[n, 9], {n, 150}] (* Vincenzo Librandi, Feb 03 2016 *)

PROG

(Scheme)

(define (A264981 n) (let loop ((k 9)) (if (not (zero? (modulo n k))) (/ k 9) (loop (* 9 k)))))

(PARI) a(n) = 9^valuation(n, 9); \\ Michel Marcus, Dec 08 2015

(Sage) [9^valuation(i, 9) for i in [1..100]] # Tom Edgar, Feb 02 2016

CROSSREFS

Cf. A264979.

Similar sequences for other bases: A006519 (2), A038500 (3), A234957 (4), A060904 (5), A234959 (6).

Sequence in context: A010534 A078297 A189788 * A113061 A284099 A176410

Adjacent sequences:  A264978 A264979 A264980 * A264982 A264983 A264984

KEYWORD

nonn,mult

AUTHOR

Antti Karttunen, Dec 07 2015

EXTENSIONS

Keyword:mult added by Andrew Howroyd, Jul 20 2018

STATUS

approved

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Last modified November 15 14:06 EST 2019. Contains 329149 sequences. (Running on oeis4.)