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

1,2

Comments

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

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A000045, A005349, A337448.

Sequence in context: A229040 A143873 A273046 * A053056 A041157 A178356

Adjacent sequences: A117771 A117772 A117773 * A117775 A117776 A117777

Keyword

base,nonn

Author

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

Status

approved