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A071774
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Related to Pisano periods: integers k such that the period of Fibonacci numbers mod k equals 2*(k+1).
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10
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3, 7, 13, 17, 23, 37, 43, 53, 67, 73, 83, 97, 103, 127, 137, 157, 163, 167, 173, 193, 197, 223, 227, 257, 277, 283, 293, 313, 317, 337, 367, 373, 383, 397, 433, 443, 457, 463, 467, 487, 503, 523, 547, 577, 587, 593, 607, 613, 617, 643, 647, 653, 673, 683, 727
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OFFSET
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1,1
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COMMENTS
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Terms are primes with final digit 3 or 7.
If k is a term, then for m=5*k the period of Fibonacci numbers mod m equals 2*(m+5). - Matthew Goers, Jan 13 2021
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LINKS
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MATHEMATICA
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Select[Prime@ Range[129], Function[n, Mod[Last@ NestWhile[{Mod[#2, n], Mod[#1 + #2, n], #3 + 1} & @@ # &, {1, 1, 1}, #[[1 ;; 2]] != {0, 1} &], n] == Mod[2 (n + 1), n] ]] (* Michael De Vlieger, Mar 31 2021, after Leo C. Stein at A001175 *)
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PROG
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(PARI) for(n=2, 5000, t=2*(n+1); good=1; if(fibonacci(t)%n==0, for(s=0, t, if(fibonacci(t+s)%n!=fibonacci(s)%n, good=0; break); if(s>1&&s<t-1&&fibonacci(s)%n==0, cur=s; good2=1; for(ss=0, s, if(fibonacci(ss+s)%n!=fibonacci(ss)%n, good2=0; break)); if(good2, good=0; break); ); ); if(good, print1(n, ", ")))) \\ Lambert Klasen (Lambert.Klasen(AT)gmx.net), Dec 21 2004
(PARI) forprime(p=3, 3000, if(p%5==2||p%5==3, a=1; b=0; c=1; while(a!=0||b!=1, c++; d=a; a=b; a=(a+d)%p; b=d%p); if(c==(2*(p+1)), print1(p", ")))) /* V. Raman, Nov 22 2012 */
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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More terms from Lambert Klasen (Lambert.Klasen(AT)gmx.net), Dec 21 2004
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STATUS
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approved
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