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A042947 Gilda's numbers: numbers n such that if a Fibonacci sequence is formed with first term = a certain absolute value between decimal digits in n (A007953) and second term = sum of decimal digits in n (A040997), then n itself occurs as a term in the sequence. 1
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; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Is this sequence infinite?

LINKS

Table of n, a(n) for n=0..40.

Russo, F. A Set of New Smarandache Functions, Sequences and Conjectures in Numer Theory., Lupton, AZ: American Research Press, 2000.

FORMULA

Let [x1.x2.x3. ... .xi] be the decimal expansion of n. Then define F(0) = |x1-x2-...-xi|, F(1) = x1 + x2 + x3 + ... + xi, and for k>1, F(k) = F(k-1) + F(k-2). If F(k)=n for some k, then n belongs to the sequence.

PROG

(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

CROSSREFS

Cf. A007953, A038868, A040997.

Sequence in context: A108258 A232236 A228585 * A134555 A164075 A117328

Adjacent sequences:  A042944 A042945 A042946 * A042948 A042949 A042950

KEYWORD

base,nonn

AUTHOR

Felice Russo

EXTENSIONS

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

STATUS

approved

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Last modified November 14 04:40 EST 2018. Contains 317161 sequences. (Running on oeis4.)