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%I #27 Dec 11 2023 09:49:24
%S 0,5,10,15,20,25,30,35,40,45,1,6,11,16,21,26,31,36,41,46,2,7,12,17,22,
%T 27,32,37,42,47,3,8,13,18,23,28,33,38,43,48,4,9,14,19,24,29,34,39,44,
%U 49,5,10,15,20,25,30,35,40,45,50,6,11,16,21,26,31,36,41,46,51,7
%N a(n) = floor(n/10) + (5 times last digit of n).
%C If the resulting number is divisible by 7, then n is divisible by 7; (re)discovered by 12-year-old Nigerian Chika Ofili.
%D L. E. Dickson, History of the theory of numbers. Vol. I: Divisibility and primality. Chelsea Publishing Co., New York 1966.
%D A. Zbikowski, Note sur la divisibilité des nombres, Bull. Acad. Sci. St. Petersbourg 3 (1861) 151153.
%H D. B. Eperson, <a href="https://www.jstor.org/stable/30214392">Puzzles, Pastimes, Problems</a>, Mathematics in School Vol. 16, No. 5 (Nov., 1987), pp. 18-19, 34-35.
%H OB360 Media, <a href="https://ob360media.com/education/12-year-old-nigerian-chika-ofili-wins-special-award-for-discovering-a-new-mathematics-formula">12-year-old Nigerian Chika Ofili wins special award for discovering a new Mathematics formula</a>, November 2019.
%H Skeptics Stack Exchange, <a href="https://skeptics.stackexchange.com/questions/45431/is-chika-ofilis-method-for-checking-divisibility-for-7-a-new-discovery-in-mat">Is Chika Ofili's method for checking divisibility for 7 a “new discovery” in math?</a>.
%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,0,1,-1).
%F From _Stefano Spezia_, Aug 11 2020: (Start)
%F O.g.f.: x*(5 + 5*x + 5*x^2 + 5*x^3 + 5*x^4 + 5*x^5 + 5*x^6 + 5*x^7 + 5*x^8 - 44*x^9)/(1 - x - x^10 + x^11).
%F a(n) = a(n-1) + a(n-10) - a(n-11) for n > 10. (End)
%t Table[Floor[n/10]+5Mod[n,10],{n,0,80}] (* or *) LinearRecurrence[{1,0,0,0,0,0,0,0,0,1,-1},{0,5,10,15,20,25,30,35,40,45,1},80] (* _Harvey P. Dale_, Nov 01 2023 *)
%o (PARI) a(n) = 5*(n % 10) + (n\10);
%Y Cf. A008589.
%K nonn,base,easy
%O 0,2
%A _Michel Marcus_, Aug 11 2020
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