A081502 Let n = 10x + y where 0 <= y <= 9, x >= 0. Then a(n) = 3x+y.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 21, 22, 23, 24, 25, 26, 27, 28, 29

Offset: 0

Author

N. J. A. Sloane, Apr 22 2003

Keywords

• nonn
• easy

Comments

Eswaran observes that n is divisible by 7 iff repeated application of a ends at the number 7.

a(n) is divisible by 7 iff n is divisible by 7: e.g., a(7) = a(14) = a(21) = 7, a(28) = a(35) = a(42) = 14 etc. - Zak Seidov, Mar 19 2014

References

• R. Eswaran, Test of divisibility of the number 7, Abstracts Amer. Math. Soc., 23 (No. 2, 2002), #974-00-5, p. 275.

Links

• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,1,-1).

Crossrefs

Different from A028898 for n>=100 (e.g. a(111) = 34, A029989(111) = 13).

Cf. A081503, A081594, A081595, A081596, A081597, A081598, A081599, A081600.

Programs

Maple

A081502 := proc(n)
    local x,y ;
    y := modp(n,10) ;
    x := iquo(n,10) ;
    3*x+y ;
end proc:
seq(A081502(n),n=0..120) ; # R. J. Mathar, Oct 03 2014

Mathematica

Table[n - 7 * Floor[n / 10], {n, 0, 100}] (* Joshua Oliver, Dec 04 2019 *)

PARI

a(n) = 3*(n\10) + (n % 10); \\ Michel Marcus, Mar 19 2014

PARI

a(n) = [3,1]*divrem(n,10); \\ Kevin Ryde, Dec 04 2019

Formula

G.f.: -x*(6*x^9-x^8-x^7-x^6-x^5-x^4-x^3-x^2-x-1) / (x^11-x^10-x+1). - Colin Barker, Mar 19 2014

a(n) = n-7*floor(n/10). - Wesley Ivan Hurt, May 12 2016