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Smallest even number with digit sum n.
20

%I #29 Sep 15 2020 20:47:58

%S 10,2,12,4,14,6,16,8,18,28,38,48,58,68,78,88,98,198,298,398,498,598,

%T 698,798,898,998,1998,2998,3998,4998,5998,6998,7998,8998,9998,19998,

%U 29998,39998,49998,59998,69998,79998,89998,99998,199998,299998,399998,499998

%N Smallest even number with digit sum n.

%H Chai Wah Wu, <a href="/A069532/b069532.txt">Table of n, a(n) for n = 1..8999</a>

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,10,-10).

%F From _Chai Wah Wu_, Sep 15 2020: (Start)

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

%F 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)

%F a(n) = 2 * A077491(n). - _Alois P. Heinz_, Sep 15 2020

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

%o (PARI) a(n) = {my(k = 2); while(sumdigits(k) != n, k+=2); k;} \\ _Michel Marcus_, Mar 18 2016

%Y Cf. A069521 to A069530.

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

%Y Cf. A077491.

%K base,nonn,easy

%O 1,1

%A _Amarnath Murthy_, Apr 01 2002

%E More terms from _Ray Chandler_, Jul 28 2003