

A169612


Powers of 2 added sequentially to an initial value of 1 in producing A168612, which is a greedy listing of numbers all relatively prime to each other in binary.


1



1, 2, 4, 5, 8, 9, 10, 13, 14, 23, 24, 25, 30, 31, 32, 33, 38, 39, 40, 41, 46, 47, 48, 49, 54, 55, 60, 65, 70, 71, 72, 89, 90, 91, 92, 93, 94, 95, 120, 129, 146, 163, 164, 165, 182, 247, 264, 297, 298, 347, 396, 445, 446, 495, 544, 545, 578, 595, 612, 629, 646, 647, 648
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OFFSET

1,2


COMMENTS

The last term is a(552) = 16001. Any larger additional power of 2 added yields a number divisible by a prime no larger than 257 that is already included as a factor.
First computed using the online Java program in the links; the below PARI program computes all terms in about 45 seconds.  James G. Merickel, Aug 08 2015


LINKS

James G. Merickel, Table of n, a(n) for n = 1..552
Dario Alejandro Alpern, Factorization using the Elliptic Curve Method


EXAMPLE

a(5) = 8 means that with a(1)a(4) known to be 1, 2, 4 and 5  corresponding to the relatively prime values 3 = 1 + 2^1, 7 = 3 + 2^2, 23 = 7 + 2^4 and 55 = 23 + 2^5  55 + 2^6 = 119 has a factor of 7 and 55 + 2^7 = 183 has a factor of 3, but 55 + 2^8 = 311 is relatively prime to all of 3, 7, 23 and 55.


PROG

(PARI)
{
x=[1]; k=1; j=1; e=2; y=1; while(1,
n=e+y; f=1; for(i=1, j,
if(gcd(x[i], n)!=1, f=0; break()));
if(f,
print1(k" "); y+=e; x=concat(x, y); j++);
e+=e; k++)
}


CROSSREFS

Cf. A168612.
Sequence in context: A022549 A045704 A351723 * A084581 A121996 A269176
Adjacent sequences: A169609 A169610 A169611 * A169613 A169614 A169615


KEYWORD

fini,full,nonn,base


AUTHOR

James G. Merickel, Dec 03 2009


EXTENSIONS

Name edited by James G. Merickel, Aug 07 2015


STATUS

approved



