A270600 a(n) is the smallest k > 1 not already in the sequence such that p = prime(n) is a factor of 2^k-1.

2, 4, 3, 10, 12, 8, 18, 11, 28, 5, 36, 20, 14, 23, 52, 58, 60, 66, 35, 9, 39, 82, 22, 48, 100, 51, 106, 72, 56, 7, 130, 68, 138, 148, 15, 104, 162, 83, 172, 178, 180, 95, 96, 196, 99, 210, 37, 226, 76, 29

Offset: 2

Author

Felix Fröhlich, Mar 20 2016

Keywords

• nonn

Comments

First differs from A014664 at n = 24.

a(n) is the smallest r such that p = prime(n) appears in row r of A060443 and r has not been the smallest such r for any previous p.

6 is not a term of the sequence, since 2^6-1 = 3^2 * 7, but 3 and 7 are already factors of 2^4-1 and 2^3-1 respectively.

Apart from 6, are there any other k > 1 that are not terms of the sequence?

Links

• Felix Fröhlich, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A014664, A060443.

Programs

PARI

nextk(p, k) = my(kk=k+1); while(Mod(2, p)^kk!=1, kk++); kk
isinvec(v, k) = for(x=1, #v, if(v[x]==k, return(1))); return(0)
addtovec(v, k) = my(w=vector(1)); w[1]=k; v=concat(v, w); v
addnextknotinvec(v, p) = my(kk=2); while(isinvec(v, kk), kk=nextk(p, kk)); addtovec(v, kk)
my(i=0, v=[], p=3); while(i < 50, v=addnextknotinvec(v, p); p=nextprime(p+1); i++); v