A326612 - OEIS

%I #28 Jul 19 2019 20:25:36

%S 1,2,3,5,6,10,25,30,50,98,125,150,206,243,250,490,566,590,625,750,

%T 1030,1046,1094,1154,1214,1226,1250,2450,2738,2830,2846,2894,2906,

%U 3086,3125,3750,4802,5534,5594,5606,5666,5714,5770,5834,5906,5990,6070,6130,6250

%N Indices where A001175 (Pisano period) sets a new record value.

%C Record values: 1, 3, 8, 20, 24, 60, 100, 120, 300, 336, 500, 600, 624, 648, 1500, 1680, 1704, 1740, 2500, 3000, ...

%H Chai Wah Wu, <a href="/A326612/b326612.txt">Table of n, a(n) for n = 1..10000</a> (n = 1..1547 from Richard N. Smith)

%o (PARI) fibmod(n, m)=((Mod([1, 1; 1, 0], m))^n)[1, 2]

%o 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 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 a(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 print1(r=1); for(n=2, 1000, if(a(n)>r, r=a(n); print1(", "n))) \\ after _Charles R Greathouse IV_ in A001175

%Y Cf. A001175.

%K nonn

%O 1,2

%A _Richard N. Smith_, Jul 14 2019