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 A237517 Pisano period of n^2 divided by Pisano period of n. 5
 1, 2, 3, 4, 5, 1, 7, 8, 9, 5, 11, 1, 13, 7, 15, 16, 17, 9, 19, 10, 21, 11, 23, 4, 25, 13, 27, 7, 29, 5, 31, 32, 33, 17, 35, 9, 37, 19, 39, 40, 41, 7, 43, 44, 45, 23, 47, 16, 49, 25, 17, 26, 53, 27, 55, 14, 19, 29, 59, 5, 61, 31, 63, 64, 65, 11, 67, 34, 23 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS For all n, a(n) | n. Conjecture (Saha & Karthik): a(n) = 1 only for n = 1, 6, and 12. LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 Arpan Saha and C. S. Karthik, A few equivalences of Wall-Sun-Sun prime conjecture, arXiv:1102.1636 [math.NT], 2011. MATHEMATICA pp[1] = 1; pp[n_] := For[k = 1, True, k++, If[Mod[Fibonacci[k], n] == 0 && Mod[Fibonacci[k+1], n] == 1, Return[k]]]; a[n_] := pp[n^2]/pp[n]; Array[a, 100] (* Jean-François Alcover, Dec 04 2018 *) PROG (PARI) fibmod(n, m)=((Mod([1, 1; 1, 0], m))^n)[1, 2] entry_p(p)=my(k=1, c=Mod(1, p), o); while(c, [o, c]=[c, c+o]; k++); k entry(n)=if(n==1, return(1)); my(f=factor(n), v); v=vector(#f~, i, if(f[i, 1]>1e14, entry_p(f[i, 1]^f[i, 2]), entry_p(f[i, 1])*f[i, 1]^(f[i, 2] - 1))); if(f[1, 1]==2&&f[1, 2]>1, v[1]=3<

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Last modified November 27 04:58 EST 2021. Contains 349346 sequences. (Running on oeis4.)