A258827 -id:A258827 - 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

A258768 Fixed points in A258767.

Original entry on oeis.org

1, 8, 13, 34, 45, 49, 51, 80, 86, 92, 98, 146, 163, 164, 206, 216, 266, 279, 303, 312, 333, 337, 348, 356, 359, 371, 387, 388, 398, 406, 421, 432, 445, 460, 463, 465, 509, 517, 533, 536, 546, 548, 572, 576, 585, 602, 607, 612, 624, 638, 658, 666, 669, 675, 688, 704, 711, 734, 744, 765, 771, 801, 810, 814

Offset: 1

Derek Orr, Jun 09 2015

nonn

Numbers n such that A258767(n) = n.

Also fixed points of A258827. - Reinhard Zumkeller, Jun 11 2015

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Cf. A258767, A075380, A075381, A256271, A258766.

Cf. A258827.

a258768 n = a258768_list !! (n-1)
a258768_list = [x | x <- [1..], a258767 x == x]
-- Reinhard Zumkeller, Jun 11 2015

print1(1, ", "); v=[1]; n=1; while(#v<10^3, if(!issquarefree(n^2+v[#v]^2)&&!vecsearch(vecsort(v), n), v=concat(v, n); if(n==#v, print1(n, ", ")); n=0); n++)

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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