A258767 With a(1) = 1, a(n) is the smallest number not already in the sequence such that a(n)^2 + a(n-1)^2 is not squarefree.

1, 7, 14, 2, 4, 3, 6, 8, 10, 5, 12, 9, 13, 16, 18, 15, 20, 21, 22, 11, 23, 36, 24, 26, 28, 29, 47, 46, 30, 25, 35, 40, 32, 34, 17, 19, 33, 27, 31, 42, 38, 41, 37, 39, 45, 48, 44, 50, 49, 43, 51, 54, 52, 56, 58, 59, 62, 60, 55, 65, 70, 63, 57, 66, 64, 68, 72, 69, 67, 81, 75, 78, 71, 53, 79, 97, 96, 74

Offset: 1

Author

Derek Orr, Jun 09 2015

Keywords

• nonn

Comments

Believed to be a permutation of the natural numbers.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A256271, A075380.

Cf. A258768 (fixed points).

Cf. A008966, A258827 (putative inverse).

Programs

Haskell

import Data.List (delete)
a258767 n = a258767_list !! (n-1)
a258767_list = 1 : f 1 [2..] where
   f x zs = g zs where
     g (y:ys) | a008966 (x^2 + y^2) == 1 = g ys
              | otherwise = y : f y (delete y zs)
-- Reinhard Zumkeller, Jun 11 2015

PARI

v=[1]; n=1; while(n<100, if(!issquarefree(n^2+v[#v]^2)&&!vecsearch(vecsort(v), n), v=concat(v, n); n=0); n++); v