A076310 a(n) = floor(n/10) + 4*(n mod 10).
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
Offset: 0
Keywords
Examples
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.
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).
Programs
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Haskell
a076310 n = n' + 4 * m where (n', m) = divMod n 10 -- Reinhard Zumkeller, Jun 01 2013
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Magma
[Floor(n/10)+4*(n mod 10): n in [0..75]]; // Vincenzo Librandi, Feb 27 2016
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Maple
A076310:=n->floor(n/10) + 4*(n mod 10); seq(A076310(n), n=0..100); # Wesley Ivan Hurt, Jan 30 2014
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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 *) -
PARI
a(n) = n\10 + 4*(n % 10); \\ Michel Marcus, Jan 31 2014
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
Comments