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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 22 01:28 EST 2022. Contains 350481 sequences. (Running on oeis4.)