A177220 Smallest numbers with properties: products of two distinct primes of the form a(k)=2^n*m-(2^n-1), n:0->k.

6, 26, 33, 247, 247, 634, 694, 11293, 31261, 31261, 173311, 173311, 2212801

Offset

1,1

Comments

6=2*3, 26=2*13;2*26-1=51=3*17, 33=3*11;2*33-1=65=5*13;2*65-1=4*33-3=129=3*43, 247=13*19;2*247-1=493=17*29;4*247-3=985=5*197;8*247-1=1969=11*179, 247=13*19;2*247-1=493=17*29;4*247-3=985=5*197;8*247-1=1969=11*179;16*247-15=3937=31*127, 634=2*317;2*634=1267=7*181;4*634-3=2533=17*149;8*634-7=5065=5*1013;16*634=10129=7*1447;32*634=20257=47*431, ..

Links

Table of n, a(n) for n=1..13.

Mathematica

f[n_]:=Last/@FactorInteger[n]=={1, 1}; g[n_, m_]:=Module[{a=1, x, y, z}, Do[x=2^k; y=x-1; z=x*n-y; If[ !f[z], a=0; Break[]], {k, 0, m}]; a]; q=0; e=5; lst={}; Do[e++; If[g[e, q]==1, Print[e]; AppendTo[lst, e]; q++; e-- ], {n, 0, 4*10!}]; lst

Crossrefs

Cf. A006881, A177210, A177211, A177212, A177213, A177214, A177215, A177216, A177217

Sequence in context: A038474 A043006 A076284 * A157353 A271311 A075454

Adjacent sequences: A177217 A177218 A177219 * A177221 A177222 A177223

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, May 04 2010

Status

approved