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A076310 a(n) = floor(n/10) + 4*(n mod 10). 7
0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 2, 6, 10, 14, 18, 22, 26, 30, 34, 38, 3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 7, 11, 15, 19, 23 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

(n==0 modulo 13) iff (a(n)==0 modulo 13); applied recursively, this property provides a divisibility test for numbers given in base 10 notation.

REFERENCES

Karl Menninger, Rechenkniffe, Vandenhoeck & Ruprecht in Goettingen (1961), 79A.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Eric Weisstein's World of Mathematics, Divisibility Tests.

Wikipedia, Divisibility rule

Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1).

FORMULA

a(n) = +a(n-1) +a(n-10) -a(n-11). G.f.: -x*(-4-4*x-4*x^2-4*x^3-4*x^4-4*x^5-4*x^6-4*x^7-4*x^8+35*x^9) / ( (1+x) *(x^4+x^3+x^2+x+1) *(x^4-x^3+x^2-x+1) *(x-1)^2 ). - R. J. Mathar, Feb 20 2011

EXAMPLE

435598 is not a multiple of 13, as 435598 -> 43559+4*8=43591 -> 4359+4*1=4363 -> 436+4*3=448 -> 44+4*8=76 -> 7+4*6=29=13*2+3, therefore the answer is NO.

Is 8424 divisible by 13? 8424 -> 842+4*4=858 -> 85+4*8=117 -> 11+4*7=39=13*3, therefore the answer is YES.

MAPLE

A076310:=n->floor(n/10) + 4*(n mod 10); seq(A076310(n), n=0..100); # Wesley Ivan Hurt, Jan 30 2014

MATHEMATICA

Table[Floor[n/10] + 4*Mod[n, 10], {n, 0, 100}] (* Wesley Ivan Hurt, Jan 30 2014 *)

LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1}, {0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 1}, 80] (* Harvey P. Dale, Sep 30 2015 *)

PROG

(Haskell)

a076310 n =  n' + 4 * m where (n', m) = divMod n 10

-- Reinhard Zumkeller, Jun 01 2013

(PARI) a(n) = n\10 + 4*(n % 10); \\ Michel Marcus, Jan 31 2014

(MAGMA) [Floor(n/10)+4*(n mod 10): n in [0..75]]; // Vincenzo Librandi, Feb 27 2016

CROSSREFS

Cf. A008595, A076309, A076311, A076312.

Sequence in context: A276079 A311124 A191677 * A161352 A295774 A008586

Adjacent sequences:  A076307 A076308 A076309 * A076311 A076312 A076313

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Oct 06 2002

STATUS

approved

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Last modified November 17 11:02 EST 2019. Contains 329226 sequences. (Running on oeis4.)