A069532 Smallest even number with digit sum n.

10, 2, 12, 4, 14, 6, 16, 8, 18, 28, 38, 48, 58, 68, 78, 88, 98, 198, 298, 398, 498, 598, 698, 798, 898, 998, 1998, 2998, 3998, 4998, 5998, 6998, 7998, 8998, 9998, 19998, 29998, 39998, 49998, 59998, 69998, 79998, 89998, 99998, 199998, 299998, 399998, 499998

Offset: 1

Author

Amarnath Murthy, Apr 01 2002

Keywords

• base
• nonn
• easy

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..8999
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,10,-10).

Crossrefs

Cf. A069521 to A069530.

Cf. A000918 (smallest even number with bit sum n), A051885 (smallest number with digit sum n).

Cf. A077491.

Programs

Mathematica

t={}; Do[i=2; While[Total[IntegerDigits[i]]!=n,i=i+2]; AppendTo[t,i],{n,48}]; t (* Jayanta Basu, May 18 2013 *)

PARI

a(n) = {my(k = 2); while(sumdigits(k) != n, k+=2); k;} \\ Michel Marcus, Mar 18 2016

Formula

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

a(n) = a(n-1) + 10*a(n-9) - 10*a(n-10) for n > 17.

G.f.: 2*x*(45*x^16 - 45*x^15 + 45*x^14 - 45*x^13 + 45*x^12 - 45*x^11 + 45*x^10 - 45*x^9 + 5*x^8 - 4*x^7 + 5*x^6 - 4*x^5 + 5*x^4 - 4*x^3 + 5*x^2 - 4*x + 5)/((x - 1)*(10*x^9 - 1)). (End)

a(n) = 2 * A077491(n). - Alois P. Heinz, Sep 15 2020

Extensions

More terms from Ray Chandler, Jul 28 2003