33461

Properties

Appears in sequences

• Pell numbers: a(0) = 0, a(1) = 1; for n > 1, a(n) = 2*a(n-1) + a(n-2).at n=13A000129
• Numbers k such that 2*k^2 - 1 is a square.at n=6A001653
• Markoff (or Markov) numbers: union of positive integers x, y, z satisfying x^2 + y^2 + z^2 = 3*x*y*z.at n=24A002559
• Interleave denominators (A000129) and numerators (A001333) of convergents to sqrt(2).at n=26A002965
• Primitive parts of Pell numbers.at n=12A008555
• Denominators of continued fraction convergents to sqrt(8).at n=12A041011
• Essentially a duplicate of A000129.at n=11A048624
• Primes p whose period of reciprocal equals (p-1)/7.at n=26A056212
• Prime hypotenuses of Pythagorean triangles with consecutive integer sides.at n=3A056869
• a(n) is the least natural number m such that the fractional part of m*(2^0.5) is less than 2^(-n).at n=14A058580
• a(n) is the least natural number m such that the fractional part of m*(2^0.5) is less than 2^(-n).at n=15A058580
• The next smallest pair of numbers is taken so that a(2n-1)/a(2n) converges to sqrt(2).at n=37A065375
• Define an increasing sequence as follows: Given the first term called the seed (the seed need not have the property of the sequence.), subsequent terms are defined as obtained by inserting/placing digits (at least one) in the previous term to obtain the smallest number with a given property. This is the growing prime sequence for the seed a(1) = 6.at n=4A068171
• Number of n X 12 binary arrays with a path of adjacent 1's from upper left corner to anywhere in right hand column.at n=0A069303
• Number of 2 X n binary arrays with a path of adjacent 1's from upper left corner to anywhere in right hand column.at n=10A069306
• Product representation of the Pell numbers A000129 and A002203.at n=25A072280
• a(n) is the n-th new record value in A073300.at n=33A073301
• Expansion of 1/(1 + 2*x - x^2).at n=12A077985
• a(0) = a(1) = 1; thereafter a(2*n+1) = 2*a(2*n) - a(2*n-1), a(2*n) = 4*a(2*n-1) - a(2*n-2).at n=13A079496
• Greedy frac multiples of sqrt(2): a(1)=1, Sum_{n>=0} frac(a(n)*x)=1 at x=sqrt(2).at n=17A079934