A008318 Smallest number strictly greater than previous one which is the sum of squares of two previous distinct terms (a(1)=1, a(2)=2).

1, 2, 5, 26, 29, 677, 680, 701, 842, 845, 866, 1517, 458330, 458333, 458354, 459005, 459170, 462401, 462404, 462425, 463076, 463241, 491402, 491405, 491426, 492077, 492242, 708965, 708968, 708989, 709640, 709805, 714026, 714029, 714050, 714701

Offset

1,2

Comments

A003095 is a subsequence apart from the initial term. - Reinhard Zumkeller, Jan 17 2008

The subsequence of primes begins: 2, 5, 29, 677, 701, 458333, 462401, 492077, 708989, 714029, ... - Jonathan Vos Post, Nov 21 2012

References

F. Smarandache, Definitions solved and unsolved problems, conjectures and theorems in number theory and geometry, edited by M. Perez, Xiquan Publishing House 2000

F. Smarandache, Sequences of Numbers Involved in Unsolved Problems, Hexis, Phoenix, 2006.

Links

T. D. Noe, Table of n, a(n) for n=1..1000

Mihaly Bencze [Beneze], Smarandache Recurrence Type Sequences, in Bull. Pure Appl. Sciences, Vol. 16E, No. 2, 231-236, 1997.

F. Smarandache, Definitions, Solved and Unsolved Problems, Conjectures, ...

F. Smarandache, Sequences of Numbers Involved in Unsolved Problems.

Eric Weisstein's World of Mathematics, Smarandache Sequences.

Mathematica

a[1]=1; a[2]=2; a[n_] := a[n] = First[ Select[ Sort[ Flatten[ Table[a[j]^2 + a[k]^2, {j, 1, n-1}, {k, j+1, n-1}]]], # > a[n-1] & , 1]]; Table[a[n], {n, 1, 36}](* Jean-François Alcover, Nov 10 2011 *)

Prog

(Haskell)
import Data.Set (singleton, deleteFindMin, insert)
a008318 n = a008318_list !! (n-1)
a008318_list = f [1] (singleton 1) where
   f xs s =
     m : f (m:xs) (foldl (flip insert) s' (map (+ m^2) (map (^ 2) xs)))
     where (m, s') = deleteFindMin s
-- Reinhard Zumkeller, Aug 15 2011

Crossrefs

Cf. A192476.

Sequence in context: A370555 A120767 A051771 * A365324 A204275 A160048

Adjacent sequences: A008315 A008316 A008317 * A008319 A008320 A008321

Keyword

nonn,easy,nice

Author

R. Muller

Extensions

More terms from David W. Wilson

Status

approved