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, 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

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: A045704 A368796 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