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

Author

R. Muller

Keywords

• nonn
• easy
• nice

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.

Crossrefs

Cf. A192476.

Programs

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

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 *)

Extensions

More terms from David W. Wilson