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A343117
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a(n) is the absolute difference between the Pisano periods of prime(n)^2 and prime(n).
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0
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3, 16, 80, 96, 100, 336, 576, 324, 1056, 392, 900, 2736, 1600, 3696, 1472, 5616, 3364, 3600, 8976, 4900, 10656, 6084, 13776, 3872, 18816, 5000, 21216, 7632, 11664, 8512, 32256, 16900, 37536, 6348, 21904, 7500, 49296, 53136, 55776, 59856, 31684, 16200, 36100
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OFFSET
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1,1
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COMMENTS
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a(n) = 0 if and only if prime(n) is a Wall-Sun-Sun (Fibonacci-Wieferich) prime.
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LINKS
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FORMULA
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PROG
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fibmod(n, m)=((Mod([1, 1; 1, 0], m))^n)[1, 2]
entryp(p)=my(k=p+[0, -1, 1, 1, -1][p%5+1], f=factor(k)); for(i=1, #f[, 1], for(j=1, f[i, 2], if((Mod([1, 1; 1, 0], p)^(k/f[i, 1]))[1, 2], break); k/=f[i, 1])); k
entry(n)=if(n==1, return(1)); my(f=factor(n), v); v=vector(#f~, i, if(f[i, 1]>1e14, entryp(f[i, 1]^f[i, 2]), entryp(f[i, 1])*f[i, 1]^(f[i, 2] - 1))); if(f[1, 1]==2&&f[1, 2]>1, v[1]=3<<max(f[1, 2]-2, 1)); lcm(v)
a001175(n)=if(n==1, return(1)); my(k=entry(n)); forstep(i=k, n^2, k, if(fibmod(i-1, n)==1, return(i)))
\\ (End)
a(n) = my(p=prime(n)); abs(a001175(p^2)-a001175(p))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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