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

0,2

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.

A. Zbikowski, Note sur la divisibilité des nombres, Bull. Acad. Sci. St. Petersbourg 3 (1861) 151153.

Links

Table of n, a(n) for n=0..70.

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?.

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

Cf. A008589.

Sequence in context: A182340 A313733 A076311 * A063284 A257222 A092454

Adjacent sequences: A336480 A336481 A336482 * A336484 A336485 A336486

Keyword

nonn,base,easy

Author

Michel Marcus, Aug 11 2020

Status

approved