

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
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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.
Cf. A002587, A066845, A108974.
Sequence in context: A105408 A291963 A242104 * A085418 A339944 A292008
Adjacent sequences: A158892 A158893 A158894 * A158896 A158897 A158898


KEYWORD

nice,nonn


AUTHOR

Martin Griffiths, Mar 29 2009


STATUS

approved



