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 A173656 Primes p such that p^2 divides P(p), where P = Perrin sequence A001608. 2
 521, 190699 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS It is not known if this sequence is infinite. The squares are in A013998. No more terms < 10^9. LINKS G. L. Honaker, Jr. and Chris Caldwell, Prime Curios! 521 Wikipedia, Perrin number EXAMPLE 521 is in the sequence since its square 271441 is the factor of A001608(521). MATHEMATICA lst = {}; a = 3; b = 0; c = 2; Do[P = b + a; If[PrimeQ[n] && Divisible[P, n^2], AppendTo[lst, n]]; a = b; b = c; c = P, {n, 3, 2*10^5}]; lst lst = {}; PowerMod2[mat_, n_, m_] := Mod[Fold[Mod[If[#2 == 1, #1.#1.mat, #1.#1], m] &, mat, Rest@IntegerDigits[n, 2]], m]; LinearRecurrence2[coeffs_, init_, n_, m_] := Mod[First@PowerMod2[Append[RotateRight /@ Most@IdentityMatrix@Length[coeffs], coeffs], n, m].init, m] /; n >= Length[coeffs]; Do[n = Power[p, 2]; If[PrimeQ[p] && LinearRecurrence2[{1, 1, 0}, {3, 0, 2}, n, n] == 0, AppendTo[lst, p]], {p, 1, 2*10^5, 2}]; lst PROG (PARI) /* Assuming b13998 containing second column of b013998.txt */ A013998 = readvec(b13998); for (k=1, #A013998, if (issquare(A013998[k])==1, print(k, " ", A013998[k]))); /* Hugo Pfoertner, Sep 01 2017 */ CROSSREFS Cf. A001608, A013998. Sequence in context: A167734 A122715 A153180 * A015291 A028484 A057699 Adjacent sequences:  A173653 A173654 A173655 * A173657 A173658 A173659 KEYWORD bref,hard,more,nonn AUTHOR Arkadiusz Wesolowski, Aug 15 2012 STATUS approved

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Last modified November 21 05:01 EST 2017. Contains 294988 sequences.