OFFSET
0,2
COMMENTS
If the resulting number is divisible by 7, then n is divisible by 7; (re)discovered by 12-year-old Nigerian Chika Ofili.
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).
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)
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 *)
PROG
(PARI) a(n) = 5*(n % 10) + (n\10);
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Michel Marcus, Aug 11 2020
STATUS
approved