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A173656 Primes p such that p^2 divides P(p), where P = Perrin sequence A001608. 1
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

Table of n, a(n) for n=1..2.

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

CROSSREFS

Cf. A001608.

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 August 20 20:09 EDT 2017. Contains 290837 sequences.