

A112037


Go through all of the primes p and for each one, factor p1 into primes. List the primes in order of their first appearance in the p1 factorizations.


6



2, 3, 5, 11, 7, 23, 13, 29, 41, 17, 53, 37, 83, 43, 89, 19, 113, 131, 67, 47, 73, 31, 79, 173, 179, 61, 191, 97, 233, 239, 251, 127, 139, 281, 71, 293, 101, 103, 107, 163, 59, 359, 193, 199, 137, 419, 431, 443, 151, 491, 509, 181, 109, 277, 593, 149, 307, 641, 653
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

2,1


COMMENTS

The length of this list of distinct prime factors of p1 encountered through p=prime(n) is given by A055768.  Ray Chandler, Nov 30 2005
If "p1" is changed to "p+1" we get A236388.  N. J. A. Sloane, Jan 24 2014
A permutation of the primes by Dirichlet's theorem on arithmetic progressions: for any pair (r,s) of integers such that gcd(r,s)=1 there are infinitely many primes in the sequence r + k*s; choose r=1 and s=p.  Joerg Arndt, Mar 20 2016


LINKS

Alois P. Heinz, Table of n, a(n) for n = 2..10000
Wikipedia, Dirichlet's theorem on arithmetic progressions


EXAMPLE

We start with the second prime, 3. 31 = 2, so 2 is the first term.
51 = 2*2, nothing new.
71 = 2*3 and 3 is new, so that is the second term.
111 = 2*5 and we get 5; etc.


MATHEMATICA

lst = {}; r[n_] := (len = Length@lst; lst = Flatten@ Join[lst, Select[First /@ FactorInteger[Prime@n  1], ! MemberQ[lst, # ] &]]; If[l < Length@lst, 1, 0]); Do[ r[n], {n, 214}]; lst (* Robert G. Wilson v, Nov 30 2005 *)
DeleteDuplicates[Rest[Flatten[FactorInteger[#][[All, 1]]&/@ (Prime[ Range[ 250]]1)]]] (* Harvey P. Dale, May 26 2019 *)


PROG

(PARI) g=1; forprime(p=2, 299, f=factorint(p1)[, 1]; z=factorback(f); r=z/gcd(z, g); g*=r; if(r>1, print(r, " ", p))); \\ Jack Brennen, Nov 28 2005
(GAP) Set(Flat(List(Filtered([3..1500], IsPrime), i>Factors(i1)))); # Muniru A Asiru, Dec 06 2018


CROSSREFS

Cf. A055768, A112038, A114461, A236388.
Sequence in context: A084333 A288833 A067663 * A087583 A233098 A258975
Adjacent sequences: A112034 A112035 A112036 * A112038 A112039 A112040


KEYWORD

easy,nonn


AUTHOR

Michel Dauchez (mdzdm(AT)yahoo.fr), Nov 28 2005


EXTENSIONS

Better description from Jack Brennen, Nov 28 2005
Extended by Ray Chandler and Robert G. Wilson v, Nov 30 2005


STATUS

approved



