A192525 -id:A192525 - cp's OEIS frontend

A192526 (A192525)/2.

1, 4, 19, 88, 94, 433, 439, 469, 2020, 2128, 2158, 2164, 2194, 2344, 9925, 9955, 10093, 10099, 10603, 10639, 10783, 10789, 10819, 10969, 11719, 46288, 46456, 48910, 48940, 49450, 49588, 49624, 49630, 49768, 49774, 50458, 50464, 50494, 52828

Offset: 1

Clark Kimberling, Jul 03 2011

nonn

See A192525.

Cf. A192525, A192472.

Mathematica
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(See A192525.)
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A192476 Monotonic ordering of set S generated by these rules: if x and y are in S then x^2 + y^2 is in S, and 1 is in S.

Original entry on oeis.org

1, 2, 5, 8, 26, 29, 50, 65, 68, 89, 128, 677, 680, 701, 740, 842, 845, 866, 905, 1352, 1517, 1682, 2501, 2504, 2525, 2564, 3176, 3341, 4226, 4229, 4250, 4289, 4625, 4628, 4649, 4688, 4901, 5000, 5066, 5300, 5465, 6725, 7124, 7922, 7925, 7946, 7985

Offset: 1

Clark Kimberling, Jul 01 2011

nonn

Let N denote the positive integers, and suppose that f(x,y): N x N->N. Let "start" denote a subset of N, and let S be the set of numbers defined by these rules: if x and y are in S, then f(x,y) is in S, and "start" is a subset of S. The monotonic increasing ordering of S is a sequence:
A192476:  f(x,y)=x^2+y^2, start={1}
A003586:  f(x,y)=x*y, start={1,2,3}
A051037:  f(x,y)=x*y, start={1,2,3,5}
A002473:  f(x,y)=x*y, start={1,2,3,5,7}
A003592:  f(x,y)=x*y, start={2,5}
A009293:  f(x,y)=x*y+1, start={2}
A009388:  f(x,y)=x*y-1, start={2}
A009299:  f(x,y)=x*y+2, start={3}
A192518:  f(x,y)=(x+1)(y+1), start={2}
A192519:  f(x,y)=floor(x*y/2), start={3}
A192520:  f(x,y)=floor(x*y/2), start={5}
A192521:  f(x,y)=floor((x+1)(y+1)/2), start={2}
A192522:  f(x,y)=floor((x-1)(y-1)/2), start={5}
A192523:  f(x,y)=2x*y-x-y, start={2}
A192525:  f(x,y)=2x*y-x-y, start={3}
A192524:  f(x,y)=4x*y-x-y, start={1}
A192528:  f(x,y)=5x*y-x-y, start={1}
A192529:  f(x,y)=3x*y-x-y, start={2}
A192531:  f(x,y)=3x*y-2x-2y, start={2}
A192533:  f(x,y)=x^2+y^2-x*y, start={2}
A192535:  f(x,y)=x^2+y^2+x*y, start={1}
A192536:  f(x,y)=x^2+y^2-floor(x*y/2), start={1}
A192537:  f(x,y)=x^2+y^2-x*y/2, start={2}
A192539:  f(x,y)=2x*y+floor(x*y/2), start={1}

			1^2+1^2=2, 1^2+2^2=5, 2^2+2^2=8, 1^2+5^2=26.

Reinhard Zumkeller, Table of n, a(n) for n = 1..6171

Cf. A009293, A008318.

import Data.Set (singleton, deleteFindMin, insert)
a192476 n = a192476_list !! (n-1)
a192476_list = f [1] (singleton 1) where
   f xs s =
     m : f xs' (foldl (flip insert) s' (map (+ m^2) (map (^ 2) xs')))
     where xs' = m : xs
           (m,s') = deleteFindMin s
-- Reinhard Zumkeller, Aug 15 2011

start = {1}; f[x_, y_] :=  x^2 + y^2  (* start is a subset of t, and if x,y are in t then f(x,y) is in t. *)
b[z_] :=  Block[{w = z}, Select[Union[Flatten[AppendTo[w, Table[f[w[[i]], w[[j]]], {i, 1, Length[w]}, {j, 1, i}]]]], # < 30000 &]];
t = FixedPoint[b, start] (* A192476 *)
Differences[t]
(* based on program by Robert G. Wilson v at A009293 *)

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A192526 (A192525)/2.

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