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Search: id:A117774
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| A117774 |
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Fibonacci numbers which are divisible by the sum of their digits. |
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+0
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| 1, 2, 3, 5, 8, 21, 144, 2584, 14930352, 86267571272, 498454011879264, 160500643816367088, 114059301025943970552219, 5358359254990966640871840, 555565404224292694404015791808, 1226132595394188293000174702095995
(list; graph; listen)
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OFFSET
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1,2
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EXAMPLE
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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.
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MAPLE
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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 (deutsch(AT)duke.poly.edu), Apr 16 2006
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PROGRAM
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(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)
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CROSSREFS
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Cf. A000045.
Adjacent sequences: A117771 A117772 A117773 this_sequence A117775 A117776 A117777
Sequence in context: A002363 A041457 A143873 this_sequence A053056 A041157 A042785
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KEYWORD
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base,nonn
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AUTHOR
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Luc Stevens (lms022(AT)yahoo.com), Apr 15 2006
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EXTENSIONS
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a(11) to a(16) from Emeric Deutsch (deutsch(AT)duke.poly.edu) and Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Apr 16 2006
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