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Search: id:A042947
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| A042947 |
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Gilda's numbers: if a Fibonacci sequence is formed with first term = absolute value between decimal digits in n and second term = sum of decimal digits in n, then n itself occurs as a term in the sequence. |
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+0
2
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| 0, 29, 49, 78, 110, 152, 220, 314, 330, 364, 440, 550, 628, 660, 683, 770, 880, 990, 997, 2207, 5346, 13064, 30254, 35422, 37862, 38006, 65676, 73805, 143662, 202196, 933138, 977909, 3120796, 3242189, 3363582, 3606368, 3727761, 3849154, 3970547, 4484776, 4848955
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Is this sequence infinite?
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LINKS
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Russo, F. A Set of New Smarandache Functions, Sequences, and Conjectures in Numer Theory., Lupton, AZ: American Research Press, 2000.
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FORMULA
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Let be n=x1x2x3...xi in base 10. Then F(0)=|x1-x2..-xi|, F(1)=x1+x2+x3..+xi......F(k)=F(k-1)+F(k-2). If F(k)=n then n belong to the sequence.
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PROGRAM
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(PARI) for(n=0, 10000000, s=eval(Vec(Str(n))); f1=sum(i=1, #s, s[i]); f0=abs(2*s[1]-f1); f=f0+f1; while(f<=n, if(f==n, print1(n", "); break); f0=f1; f1=f; f=f0+f1)) -Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 30 2008
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CROSSREFS
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Cf. A038868.
Adjacent sequences: A042944 A042945 A042946 this_sequence A042948 A042949 A042950
Sequence in context: A106754 A063642 A108258 this_sequence A134555 A117328 A105406
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KEYWORD
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base,nonn
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AUTHOR
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Felice Russo (felice.russo(AT)katamail.com)
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EXTENSIONS
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Corrected and extended by Larry Reeves (larryr(AT)acm.org), Sep 28 2000
2 more terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 30 2008
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