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A326612 Indices where A001175 (Pisano period) sets a new record value.

%I A326612 #28 Jul 19 2019 20:25:36
%S A326612 1,2,3,5,6,10,25,30,50,98,125,150,206,243,250,490,566,590,625,750,
%T A326612 1030,1046,1094,1154,1214,1226,1250,2450,2738,2830,2846,2894,2906,
%U A326612 3086,3125,3750,4802,5534,5594,5606,5666,5714,5770,5834,5906,5990,6070,6130,6250
%N A326612 Indices where A001175 (Pisano period) sets a new record value.
%C A326612 Record values: 1, 3, 8, 20, 24, 60, 100, 120, 300, 336, 500, 600, 624, 648, 1500, 1680, 1704, 1740, 2500, 3000, ...
%H A326612 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 A326612 (PARI) fibmod(n, m)=((Mod([1, 1; 1, 0], m))^n)[1, 2]
%o A326612 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 A326612 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 A326612 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 A326612 print1(r=1); for(n=2, 1000, if(a(n)>r, r=a(n); print1(", "n))) \\ after _Charles R Greathouse IV_ in A001175
%Y A326612 Cf. A001175.
%K A326612 nonn
%O A326612 1,2
%A A326612 _Richard N. Smith_, Jul 14 2019