A336483 a(n) = floor(n/10) + (5 times last digit of n).
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, 27, 32, 37, 42, 47, 3, 8, 13, 18, 23, 28, 33, 38, 43, 48, 4, 9, 14, 19, 24, 29, 34, 39, 44, 49, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 6, 11, 16, 21, 26, 31, 36, 41, 46, 51, 7
Offset: 0
References
- L. E. Dickson, History of the theory of numbers. Vol. I: Divisibility and primality. Chelsea Publishing Co., New York 1966.
Links
- D. B. Eperson, Puzzles, Pastimes, Problems, Mathematics in School Vol. 16, No. 5 (Nov., 1987), pp. 18-19, 34-35.
- OB360 Media, 12-year-old Nigerian Chika Ofili wins special award for discovering a new Mathematics formula, November 2019.
- Skeptics Stack Exchange, Is Chika Ofili's method for checking divisibility for 7 a “new discovery” in math?.
- A. Zbikowski, Note sur la divisibilité des nombres, Bull. Acad. Sci. St. Petersbourg 3 (1861) pp. 151-153.
- 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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Mathematica
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 *) -
PARI
a(n) = 5*(n % 10) + (n\10);
Formula
From Stefano Spezia, Aug 11 2020: (Start)
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).
a(n) = a(n-1) + a(n-10) - a(n-11) for n > 10. (End)
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