A172143 (A172126(n) - 1)/3.

0, 1, 3, 5, 13, 21, 28, 53, 85, 113, 213, 227, 341, 453, 853, 909, 1365, 1813, 1820, 3413, 3637, 5461, 7253, 7281, 13653, 14549, 14563, 21845, 29013, 29125, 54613, 58197, 58253, 87381

Offset

1,3

Comments

Conjecture: sequence consists of an infinite number of subsequences S(m,0) = A172241(n) = (1/18)[8^n-(-1)^n-9], m>0, S(m,n+1) = 4*S(m,n)+1. The first subsequences

S(1,n) = A002450(n) = (4^n-1)/3 = = 0,1,5,21,85...,

S(2,n) = A072197(n) = (10*4^n-1)/3 = 3,13,53,213...,

S(3,n) = (85*4^n-1)/3 = 28,113,453...,

S(4,n) = (682*4^n-1)/3 = 227,909,3637..., and generally,

S(m,n) = [(3*A172241(m)+1)*4^n-1]/3.

Links

Table of n, a(n) for n=1..34.

Prog

(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-1)/3, ", ")))

Crossrefs

Sequence in context: A034484 A290441 A222752 * A218790 A168388 A059872

Adjacent sequences: A172140 A172141 A172142 * A172144 A172145 A172146

Keyword

nonn

Author

Ralf Stephan, Nov 19 2010

Status

approved