A117774 Fibonacci numbers which are divisible by the sum of their digits.

1, 2, 3, 5, 8, 21, 144, 2584, 14930352, 86267571272, 498454011879264, 160500643816367088, 114059301025943970552219, 5358359254990966640871840, 555565404224292694404015791808, 1226132595394188293000174702095995, 18547707689471986212190138521399707760

Offset: 1

Author

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

Keywords

• base
• nonn

Comments

Intersection of A005349 and A000045. - Michel Marcus, Jul 11 2016

Examples

			2584 is in the sequence because (1) it is a Fibonacci number, (2) the sum of its digits is 2+5+8+4=19 and 2584 is divisible by 19.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..64

Crossrefs

Cf. A000045, A005349, A337448.

Programs

Maple

with(combinat): a:=proc(n) local ff, sod: ff:=convert(fibonacci(n),base,10): sod:=add(ff[j],j=1..nops(ff)): if type(fibonacci(n)/sod,integer)=true then fibonacci(n) else fi end: seq(a(n),n=2..180); # Emeric Deutsch, Apr 16 2006

Mathematica

Select[Fibonacci[Range[2,250]],Divisible[#,Total[IntegerDigits[#]]]&] (* Harvey P. Dale, May 06 2013 *)

PARI

{m=170; for(n=2,m,a=fibonacci(n); s=0; k=a; while(k>0, d=divrem(k,10); k=d[1]; s=s+d[2]); if(a%s==0,print1(a,",")))} \\ Klaus Brockhaus, Apr 16 2006

Extensions

a(11) to a(16) from Emeric Deutsch and Klaus Brockhaus, Apr 16 2006

a(17) from Harvey P. Dale, May 06 2013