

A090956


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


3



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
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OFFSET

0,2


COMMENTS

a(n) > a(n1), a(n) + a(n1) is a square, a(n)  a(n1) 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



