A117789 Lucas numbers which are divisible by the sum of their digits.

1, 3, 4, 7, 18, 322, 5778, 505019158607, 84722519070079276, 1473646213395791149646646123, 105249261265075663875711417309855979021650214636

Offset: 1

Author

Luc Stevens (lms022(AT)yahoo.com), Apr 15 2006

Keywords

• base
• nonn

Comments

a(12) has 83 digits and it is too large to include in the data section. - Amiram Eldar, Feb 08 2021

Examples

			322 is in the sequence because it is a Lucas number and it is divisible by the sum of its digits, 3+2+2 = 7.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..17

Crossrefs

Intersection of A000204 and A005349.

Cf. A337449.

Programs

Mathematica

Select[LinearRecurrence[{1, 1}, {1, 3}, 230], Divisible[#, Plus @@ IntegerDigits[#]] &] (* Amiram Eldar, Feb 08 2021 *)

PARI

{m=370;a=1;b=3;print1(a,",",b,",");for(n=3,m,c=b+a;a=b;b=c;s=0;k=b;while(k>0,d=divrem(k,10);k=d[1];s=s+d[2]);if(b%s==0,print1(b,",")))} \\ Klaus Brockhaus, Apr 17 2006

Formula

a(n) = A000204(A337449(n+1)). - Amiram Eldar, Feb 08 2021

Extensions

a(9) corrected, a(10) and a(11) from Klaus Brockhaus, Apr 17 2006