A172126 Terms of A181666 of the form 3*k+1.

1, 4, 10, 16, 40, 64, 85, 160, 256, 340, 640, 682, 1024, 1360, 2560, 2728, 4096, 5440, 5461, 10240, 10912, 16384, 21760, 21844, 40960, 43648, 43690, 65536, 87040, 87376, 163840, 174592, 174760, 262144, 348160, 349504, 349525, 655360, 698368, 699040, 1048576, 1392640

Offset: 1

Author

Ralf Stephan, Nov 19 2010

Keywords

• nonn

Comments

Numbers of the form 2^m*(4^k-1)/3 and, simultaneously, of the form 3*j+1, for k>0, j,m>=0.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A181666.

Programs

Mathematica

seq[max_] := Module[{kmax = Floor[Log[4, 3*max+1]], s = {}, s1, odd},Do[odd = (4^k-1)/3; s1 = 2^Range[0, Floor[Log2[max/odd]]] * odd; s = Join[s, s1], {k, 1, kmax}]; Select[Union[s], Mod[#, 3] == 1 &]]; seq[1500000] (* Amiram Eldar, Aug 31 2024 *)

PARI

for(n=1, 300000, o=3*n/2^valuation(n, 2)+1; b=ispower(o); if(b&&b%2==0&&round(sqrtn(o, b/2))==4&&(n-1)%3==0, print1(n, ", ")))

Extensions

More terms from Amiram Eldar, Aug 31 2024