A258768 -id:A258768 - cp's OEIS frontend

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

Derek Orr, Jun 09 2015

nonn

Believed to be a permutation of the natural numbers.

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

Cf. A256271, A075380.
Cf. A258768 (fixed points).
Cf. A008966, A258827 (putative inverse).

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

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

A258827 Smallest m such that A258767(m) = n.

Original entry on oeis.org

1, 4, 6, 5, 10, 7, 2, 8, 12, 9, 20, 11, 13, 3, 16, 14, 35, 15, 36, 17, 18, 19, 21, 23, 30, 24, 38, 25, 26, 29, 39, 33, 37, 34, 31, 22, 43, 41, 44, 32, 42, 40, 50, 47, 45, 28, 27, 46, 49, 48, 51, 53, 74, 52, 59, 54, 63, 55, 56, 58, 84, 57, 62, 65, 60, 64, 69

Offset: 1

Reinhard Zumkeller, Jun 11 2015

nonn

If A258767 is a permutation, this sequence is its inverse.

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

Cf. A258767, A258768 (fixed points).

import Data.List (elemIndex); import Data.Maybe (fromJust)
a258827 = (+ 1) . fromJust . (`elemIndex` a258767_list)

cp's OEIS Frontend

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.

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