login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

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

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

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