A069534 Smallest multiple of 5 with digit sum n.

10, 20, 30, 40, 5, 15, 25, 35, 45, 55, 65, 75, 85, 95, 195, 295, 395, 495, 595, 695, 795, 895, 995, 1995, 2995, 3995, 4995, 5995, 6995, 7995, 8995, 9995, 19995, 29995, 39995, 49995, 59995, 69995, 79995, 89995, 99995, 199995, 299995, 399995, 499995, 599995

Offset

1,1

Comments

a(6) onwards the pattern is evident.

Links

Table of n, a(n) for n=1..46.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,10,-10).

Formula

a(n) = ((n+4)%9+1)*10^floor((n+4)/9)-5 for all n > 4, where % is the binary mod/remainder operator. - M. F. Hasler, Sep 16 2016

From Chai Wah Wu, Sep 15 2020: (Start)

a(n) = a(n-1) + 10*a(n-9) - 10*a(n-10) for n > 14.

G.f.: 5*x*(72*x^13 - 18*x^12 - 18*x^11 - 18*x^10 - 18*x^9 + 2*x^8 + 2*x^7 + 2*x^6 + 2*x^5 - 7*x^4 + 2*x^3 + 2*x^2 + 2*x + 2)/((x - 1)*(10*x^9 - 1)). (End)

a(n) = 5 * A077492(n). - Alois P. Heinz, Sep 15 2020

Mathematica

t={}; Do[i=5; While[Total[IntegerDigits[i]]!=n, i=i+5]; AppendTo[t, i], {n, 46}]; t (* Jayanta Basu, May 19 2013 *)
With[{f=5*Range[200000]}, Flatten[Table[Select[f, Total[IntegerDigits[#]] == n&, 1], {n, 50}]]] (* Harvey P. Dale, Dec 31 2013 *)

Prog

(PARI) A069534(n)=(((n+4)%9+1)*10^((n+4)\9)-5)*10^(n<5) \\ M. F. Hasler, Sep 16 2016

Crossrefs

Cf. A069521 to A069530, A069532, A069533.

Cf. A077492.

Sequence in context: A291625 A172260 A300024 * A237416 A236507 A031140

Adjacent sequences: A069531 A069532 A069533 * A069535 A069536 A069537

Keyword

base,nonn,easy

Author

Amarnath Murthy, Apr 01 2002

Extensions

More terms from Ray Chandler, Jul 28 2003

Status

approved