cp's OEIS Frontend

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

%I A343117 #5 Apr 05 2021 20:41:44
%S A343117 3,16,80,96,100,336,576,324,1056,392,900,2736,1600,3696,1472,5616,
%T A343117 3364,3600,8976,4900,10656,6084,13776,3872,18816,5000,21216,7632,
%U A343117 11664,8512,32256,16900,37536,6348,21904,7500,49296,53136,55776,59856,31684,16200,36100
%N A343117 a(n) is the absolute difference between the Pisano periods of prime(n)^2 and prime(n).
%C A343117 a(n) = 0 if and only if prime(n) is a Wall-Sun-Sun (Fibonacci-Wieferich) prime.
%H A343117 Wikipedia, <a href="https://en.wikipedia.org/wiki/Wall%E2%80%93Sun%E2%80%93Sun_prime">Wall-Sun-Sun prime</a>
%F A343117 a(n) = abs(A343116(n)-A060305(n)) = abs(A001175(A001248(n))-A001175(A000040(n))).
%o A343117 (PARI) \\ After _Charles R Greathouse IV_ in A001175 (Start)
%o A343117 fibmod(n, m)=((Mod([1, 1; 1, 0], m))^n)[1, 2]
%o A343117 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
%o A343117 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)
%o A343117 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)))
%o A343117 \\ (End)
%o A343117 a(n) = my(p=prime(n)); abs(a001175(p^2)-a001175(p))
%Y A343117 Cf. A000040, A001175, A001248, A060305, A343116.
%K A343117 nonn
%O A343117 1,1
%A A343117 _Felix Fröhlich_, Apr 05 2021