A090956 Numbers in increasing order such that successive sums are squares and successive differences are squarefree.

1, 3, 6, 19, 30, 51, 70, 99, 157, 167, 233, 343, 386, 455, 506, 583, 642, 727, 794, 887, 1138, 1671, 1693, 1788, 1933, 2036, 2453, 2731, 2745, 3031, 3053, 3508, 3717, 4027, 4073, 4391, 4825, 4976, 5225, 5384, 5641, 5808, 6073, 6471, 6754, 6935, 7226, 7903

Offset

0,2

Comments

a(n) > a(n-1), a(n) + a(n-1) is a square, a(n) - a(n-1) is squarefree.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Example

103 follows 93 as 103 - 93 = 10 is squarefree and 93 + 103 = 196 = 14^2.

Mathematica

<<NumberTheory`; a = 1; Print[a]; Do[k = a + 1; While[ !(SquareFreeQ[k - a] && IntegerQ[Sqrt[k + a]]), k++ ]; a = k; Print[a], {n, 1, 100}] (* Ryan Propper, Aug 27 2005 *)

Crossrefs

Cf. A090955.

Sequence in context: A085061 A294570 A306968 * A108972 A304965 A203797

Adjacent sequences: A090953 A090954 A090955 * A090957 A090958 A090959

Keyword

nonn

Author

Amarnath Murthy, Dec 31 2003

Extensions

Corrected and extended by Ryan Propper, Aug 27 2005

Status

approved