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

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A236128 Primes p such that gpf(gpf(2^p-1)-1) = p. 2
2, 3, 5, 7, 11, 13, 29, 53 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

No more terms found up to p = 1277, 1277 being the first prime for which the complete factorization of 2^p-1 is not currently known (see GIMPS link). - Michel Marcus, Jan 20 2014

Conjecture: gpf(gpf(2^p-1)-1) = p for finitely many p.

Conjecture: gpf(lpf(2^p-1)-1) = p for infinitely many p.

Namely, for p = 2, 3, 5, 7, 11, 13, 23, 29, 37, 43, 47, 53, ... - Michael B. Porter, Jan 26 2014

Note that gpf(lpf(2^p-1)-1) = gpf(gpf(2^p-1)-1) = p for p = 2, 3, 5, 7, 11, 13, 29, 53. See DATA.

LINKS

Table of n, a(n) for n=1..8.

GIMPS, Exponent Status

EXAMPLE

For prime p=2, 2^p-1=3, gpf(3)=3, gpf(3-1)=2, so 2 is in the sequence.

For prime p=3, 2^p-1=7, gpf(7)=7, gpf(7-1)=3, so 3 is in the sequence.

MATHEMATICA

Select[Prime[Range[25]], FactorInteger[FactorInteger[2^# - 1][[-1, 1]] - 1][[-1, 1]] == # &] (* Alonso del Arte, Jan 19 2014 *)

PROG

(PARI) isok(p) = isprime(p) && (q = (vecmax(factor(2^p-1)[, 1]))) && (vecmax(factor(q-1)[, 1]) == p); \\ Michel Marcus, Jan 19 2014

CROSSREFS

Cf. A003260, A006530.

Sequence in context: A162567 A342566 A067908 * A332341 A262283 A187614

Adjacent sequences:  A236125 A236126 A236127 * A236129 A236130 A236131

KEYWORD

nonn,more

AUTHOR

Thomas Ordowski, Jan 19 2014

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 29 21:32 EST 2021. Contains 349416 sequences. (Running on oeis4.)