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

Author

Vladimir Joseph Stephan Orlovsky, May 04 2010

Keywords

• nonn

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, ..

Crossrefs

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

Programs

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