login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A158895 A list of primes written in order of their first appearance in a table of prime factorizations of 2^k+1, k=1,2,... . 1
3, 5, 17, 11, 13, 43, 257, 19, 41, 683, 241, 2731, 29, 113, 331, 65537, 43691, 37, 109, 174763, 61681, 5419, 397, 2113, 2796203, 97, 673, 251, 4051, 53, 157, 1613, 87211, 15790321, 59, 3033169, 61, 1321, 715827883 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
This sequence has the property that if a(n) appears first in the table as a prime factor of 2^m+1 for some m then a(n)=2*k*m+1 for some k.
When, for some m, 2^m+1 has more than one prime factor appearing in the table for the first time, we adopt the convention of entering them in ascending order. For example, the entries ..., 29, 113, ... both arise from 2^14+1.
LINKS
Harvey P. Dale and Charles R Greathouse IV, Table of n, a(n) for n = 1..4017 (first 650 terms from Dale)
EXAMPLE
2^1+1=3, 2^2+1=5, 2^3+1=3^2 and 2^4+1=17. Thus a(1)=3, a(2)=5 and a(3)=17, on noting that 2^3+1 contributes no new prime factors.
MATHEMATICA
DeleteDuplicates[Flatten[Table[Transpose[FactorInteger[2^k+1]][[1]], {k, 50}]]] (* Harvey P. Dale, Mar 30 2014 *)
PROG
(PARI) lista(n)=prs = Set(); for (k=1, n, f = factor(2^k+1); for (i=1, length(f~), onef = f[i, 1]; if (! setsearch(prs, onef), print1(onef, ", "); prs = setunion(prs, Set(onef)); ); ); ); \\ Michel Marcus, Apr 18 2013
(PARI) G=1; for(n=1, 500, g=gcd(f=2^n+1, G); while(g>1, g=gcd(g, f/=g)); f=factor(f)[, 1]; if(#f, for(i=1, #f, print1(f[i]", ")); G*=factorback(f))) \\ Charles R Greathouse IV, Jan 03 2018
CROSSREFS
Subsequence of A001269.
Sequence in context: A105408 A291963 A242104 * A085418 A339944 A359395
KEYWORD
nice,nonn
AUTHOR
Martin Griffiths, Mar 29 2009
STATUS
approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 26 13:41 EST 2024. Contains 370352 sequences. (Running on oeis4.)