login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A128164 Least k > 2 such that (n^k - 1)/(n-1) is prime, or 0 if no such prime exists. 9
3, 3, 0, 3, 3, 5, 3, 0, 19, 17, 3, 5, 3, 3, 0, 3, 25667, 19, 3, 3, 5, 5, 3, 0, 7, 3, 5, 5, 5, 7, 0, 3, 13, 313, 0, 13, 3, 349, 5, 3, 1319, 5, 5, 19, 7, 127, 19, 0, 3, 4229, 103, 11, 3, 17, 7, 3, 41, 3, 7, 7, 3, 5, 0, 19, 3, 19, 5, 3, 29, 3, 7, 5, 5, 3, 41, 3, 3, 5, 3, 0, 23, 5, 17, 5, 11, 7, 61, 3, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

a(n) = A084740(n) for all n except n = p-1, where p is an odd prime, for which A084740(n) = 2.

All nonzero terms are odd primes.

a(n) = 0 for n = {4,9,16,25,32,36,49,64,81,100,121,125,144,...}, which are the perfect powers with exceptions of the form n^(p^m) where p>2 and (n^(p^(m+1))-1)/(n^(p^m)-1) are prime and m>=1 (in which case a(n^(p^m))=p). - Max Alekseyev, Jan 24 2009

a(n) = 3 for n in A002384, i.e., for n such that n^2 + n + 1 is prime.

a(152) > 20000. - Eric Chen, Jun 01 2015

a(n) is the least number k such that (n^k - 1)/(n-1) is a Brazilian prime, or 0 if no such Brazilian prime exists. - Bernard Schott, Apr 23 2017

These corresponding Brazilian primes are in A285642. - Bernard Schott, Aug 10 2017

a(152) = 270217, see the top PRP link. - Eric Chen, Jun 04 2018

a(184) = 16703, a(200) = 17807, a(210) = 19819, a(306) = 26407, a(311) = 36497, a(326) = 26713, a(331) = 25033; a(185) > 66337, a(269) > 63659, a(281) > 63421, and there are 48 unknown a(n) for n <= 1024. - Eric Chen, Jun 04 2018

Six more terms found: a(522)=20183, a(570)=12907, a(684)=22573, a(731)=15427, a(820)=12043, a(996)=14629. - Michael Stocker, Apr 09 2020

LINKS

Max Alekseyev and Eric Chen, Table of n, a(n) for n = 2..184 (terms 2..151 from Max Alekseyev)

Eric Chen, Table of n, a(n) for n = 2..1024 status

H. Dubner, Generalized repunit primes, Math. Comp., 61 (1993), 927-930.

Richard Fischer, Generalized repunit primes of the form (B^N-1)/(B-1)

Top PRPs, Search by (152^n-1)/(152-1)

Top PRPs, Search by (b^n-1)/a

Eric Weisstein's World of Mathematics, Repunit

EXAMPLE

a(7) = 5 because (7^5 - 1)/6 = 2801 = 11111_7 is prime and (7^k - 1)/6 = 1, 8, 57, 400 for k = 1, 2, 3, 4. - Bernard Schott, Apr 23 2017

MATHEMATICA

Table[Function[m, If[m > 0, k = 3; While[! PrimeQ[(m^k - 1)/(m - 1)], k++]; k, 0]]@ If[Set[e, GCD @@ #[[All, -1]]] > 1, {#, IntegerExponent[n, #]} &@ Power[n, 1/e] /. {{k_, m_} /; Or[Not[PrimePowerQ@ m], Prime@ m, FactorInteger[m][[1, 1]] == 2] :> 0, {k_, m_} /; m > 1 :> n}, n] &@ FactorInteger@ n, {n, 2, 17}] (* Michael De Vlieger, Apr 24 2017 *)

PROG

(PARI) a052409(n) = my(k=ispower(n)); if(k, k, n>1)

a052410(n) = if (ispower(n, , &r), r, n)

is(n) = issquare(n) || (ispower(n) && !ispseudoprime((n^a052410(a052409(n))-1)/(n-1)))

a(n) = if(is(n), 0, forprime(p=3, 2^16, if(ispseudoprime((n^p-1)/(n-1)), return(p)))) \\ Eric Chen, Jun 01 2015, corrected by Eric Chen, Jun 04 2018, after Charles R Greathouse IV in A052409 and Michel Marcus in A052410

CROSSREFS

Cf. A084738, A065854, A084740, A084741, A065507, A084742, A066180, A084732, A285642, A085104.

Cf. A002384, A049409, A100330, A162862, A217070-A217089. (numbers b such that (b^p-1)/(b-1) is prime for prime p = 3 to 97)

Cf. A000043, A028491, A004061, A004062, A004063, A004023, A005808, A004064, A016054, A006032, A006033, A006034, A133857, A006035, A127995, A127996, A127997, A204940, A127998, A127999, A128000, A181979, A098438, A128002, A209120, A185073, A128003, A128004, A181987, A128005, A239637, A240765, A294722, A242797, A243279, A267375, A245237, A245442, A173767. (numbers n such that (b^n-1)/(b-1) is prime for b = 2 to 53)

A126589 gives locations of zeros.

Sequence in context: A084103 A036477 A330013 * A260636 A245256 A140686

Adjacent sequences:  A128161 A128162 A128163 * A128165 A128166 A128167

KEYWORD

nonn

AUTHOR

Alexander Adamchuk, Feb 20 2007

EXTENSIONS

a(18) = 25667 found by Henri Lifchitz, Sep 26 2007

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 27 18:22 EST 2020. Contains 338683 sequences. (Running on oeis4.)