A343117 a(n) is the absolute difference between the Pisano periods of prime(n)^2 and prime(n).

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

Offset: 1

Author

Felix Fröhlich, Apr 05 2021

Keywords

• nonn

Comments

a(n) = 0 if and only if prime(n) is a Wall-Sun-Sun (Fibonacci-Wieferich) prime.

Links

• Wikipedia, Wall-Sun-Sun prime

Crossrefs

Cf. A000040, A001175, A001248, A060305, A343116.

Programs

PARI

\\ After Charles R Greathouse IV in A001175 (Start)
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<
				

Formula

a(n) = abs(A343116(n)-A060305(n)) = abs(A001175(A001248(n))-A001175(A000040(n))).