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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A126263 List of primes generated by factoring successive integers in Sylvester's sequence (A000058). 6
2, 3, 7, 43, 13, 139, 3263443, 547, 607, 1033, 31051, 29881, 67003, 9119521, 6212157481, 5295435634831, 31401519357481261, 77366930214021991992277, 181, 1987, 112374829138729, 114152531605972711, 35874380272246624152764569191134894955972560447869169859142453622851 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The list is infinite and no term repeats since Sylvester's sequence is an infinite coprime sequence.

LINKS

William Stein and Ray Chandler, Table of n, a(n) for n = 1..28 (first 27 terms from William Stein)

Filip Saidak, Proof of Euclid's Theorem.

Filip Saidak, A New Proof of Euclid's Theorem, Amer. Math. Monthly, Dec 2006

EXAMPLE

2 = 2, 3 = 3, 7 = 7, 43 = 43, 1807 = 13 * 139, 3263443 = 3263443,

10650056950807 = 547 * 607 * 1033 * 31051,

113423713055421844361000443 = 29881 * 67003 * 9119521 * 6212157481,

12864938683278671740537145998360961546653259485195807 = 5295435634831 * 31401519357481261 * 77366930214021991992277.

165506647324519964198468195444439180017513152706377497841851388766535868639572406808911988131737645185443 = 181 * 1987 * 112374829138729 * 114152531605972711 * 35874380272246624152764569191134894955972560447869169859142453622851. - Jonathan Sondow, Jan 26 2014

MAPLE

a(0):=2; for n from 0 to 8 do a(n+1):=a(n)^2-a(n)+1; ifactor(%); od;

PROG

(Sage)

v=[2]

for n in range(12):

... v.append(v[-1]^2-v[-1]+1)

... print prime_divisors(v[-1]) # William Stein, Aug 26 2009

(PARI) vecprod(v)=prod(i=1, #v, v[i])

v=[2]; for(i=1, 10, v=concat(v, Set(factor(vecprod(v)+1)[, 1]))); v \\ Charles R Greathouse IV, Oct 02 2014

CROSSREFS

Cf. A000058, A007996, A236433.

Sequence in context: A260819 A000945 A261564 * A216826 A030087 A106864

Adjacent sequences:  A126260 A126261 A126262 * A126264 A126265 A126266

KEYWORD

nonn

AUTHOR

Howard L. Warth (hlw6c2(AT)umr.edu), Dec 22 2006

EXTENSIONS

Offset corrected by N. J. A. Sloane, Aug 20 2009

a(23) - a(27) from William Stein (wstein(AT)gmail.com), Aug 20 2009, Aug 21 2009

a(17) corrected by D. S. McNeil, Dec 10 2010

b-file updated at suggestion of Hans Havermann by Ray Chandler, Feb 27 2015

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 May 27 11:06 EDT 2018. Contains 304690 sequences. (Running on oeis4.)