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Search: id:A060305
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| A060305 |
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Related to Pisano periods: period of Fibonacci numbers mod prime(n). |
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+0
5
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| 3, 8, 20, 16, 10, 28, 36, 18, 48, 14, 30, 76, 40, 88, 32, 108, 58, 60, 136, 70, 148, 78, 168, 44, 196, 50, 208, 72, 108, 76, 256, 130, 276, 46, 148, 50, 316, 328, 336, 348, 178, 90, 190, 388, 396, 22, 42, 448, 456, 114, 52, 238, 240, 250, 516, 176, 268, 270, 556
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Assuming Wall's conjecture (which is still open) allows one to calculate A001175(m) when m is a prime power since for any k>=1 : A001175(prime(n)^k)=a(n)*prime(n)^(k-1). For example : A001175(2^k)=3*2^(k-1)=A007283(k-1)
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REFERENCES
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D. D. Wall, Fibonacci Series modulo m, American Mathematical Monthly, Vol. 67 - Jun/Jul 1960, pp. 525-532
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..1000
A. Elsenhans, J. Jahnel, The Fibonacci sequence modulo p^2 -- An investigation by computer for p < 10^14, (2004)
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MATHEMATICA
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Table[p=Prime[n]; a={1, 0}; a0=a; k=0; While[k++; s=Mod[Plus@@a, p]; a=RotateLeft[a]; a[[2]]=s; a!=a0]; k, {n, 100}] - T. D. Noe (noe(AT)sspectra.com), Jun 12 2006
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PROGRAM
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(PARI) for(n=1, 100, s=1; while(sum(i=n, n+s, abs(fibonacci(i)%prime(n)-fibonacci(i+s)%prime(n)))+sum(i=n+1, n+1+s, abs(fibonacci(i)%prime(n)-fibonacci(i+s)%prime(n)))>0, s++); print1(s, ", "))
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CROSSREFS
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Cf. A001175, A000961.
Cf. A071774, A003147.
Adjacent sequences: A060302 A060303 A060304 this_sequence A060306 A060307 A060308
Sequence in context: A018032 A086808 A047093 this_sequence A009141 A090069 A027299
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KEYWORD
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nonn
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AUTHOR
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Louis Mello (mellols(AT)aol.com), Mar 26 2001
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EXTENSIONS
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Corrected by Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 04 2002
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