A167906 -id:A167906 - cp's OEIS frontend

A167904 A121878(A121878(n)).

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 16, 14, 13, 15, 17, 18, 19, 20, 21, 22, 23, 24, 27, 28, 25, 26, 29, 30, 33, 34, 31, 32, 35, 36, 37, 39, 40, 38, 41, 42, 43, 44, 45, 46, 47, 48, 49, 51, 52, 50, 53, 54, 55, 56, 57, 58, 60, 59, 62, 61, 63, 64, 65, 66, 67, 69, 70, 68, 71, 72

Offset: 1

Reinhard Zumkeller, Nov 15 2009

nonn

Permutation of positive integers;
a(A167906(n)) = A167906(n);
a(A167905(n)) = A167905(a(n)) = A121878(n).

Index entries for sequences that are permutations of the natural numbers

A167905 Inverse integer permutation to A121878.

Original entry on oeis.org

1, 2, 3, 4, 6, 5, 8, 7, 10, 9, 12, 11, 16, 14, 13, 15, 17, 18, 19, 20, 21, 22, 24, 23, 26, 27, 28, 25, 30, 29, 34, 31, 32, 33, 35, 36, 37, 39, 40, 38, 43, 42, 41, 44, 45, 46, 47, 48, 49, 51, 52, 50, 54, 53, 56, 55, 58, 57, 62, 61, 59, 60, 63, 64, 65, 66, 67, 69, 70, 68, 72, 71

Offset: 1

Reinhard Zumkeller, Nov 15 2009

nonn

a(A167906(n)) = A167906(n);
a(A121878(n)) = A121878(a(n)) = n;
a(A167904(n)) = A167904(a(n)) = A121878(n).

Index entries for sequences that are permutations of the natural numbers

A258766 Fixed points in A256271.

Original entry on oeis.org

1, 2, 3, 26, 32, 34, 37, 49, 55, 62, 64, 74, 75, 76, 77, 164, 171, 189, 224, 273, 279, 280, 285, 303, 333, 345, 356, 363, 368, 382, 399, 411, 416, 422, 429, 430, 435, 441, 453, 470, 472, 483, 494, 524, 539, 561, 566, 579, 580, 585, 603, 609, 621, 644, 662, 666, 674, 693, 704, 715, 737, 771, 777, 794, 803

Offset: 1

Derek Orr, Jun 09 2015

Numbers n such that A256271(n) = n.
From Robert Israel, Jul 16 2019: (Start)
A necessary condition for n to be in the sequence is that A256271(n)-n is even.  When A256271(n) is even, A256271(n+1) must be odd; when A256271(n) is odd, A256271(n+1) may be either even or odd, but it appears that it is nearly always even.
The result is that we have long intervals where A256271(n)-n is even (e.g. 3369 to 22635), in which members of this sequence are relatively common, and long intervals where A256271(n)-n is odd (e.g. 22636 to 67110) which contain no members of this sequence. (End)

Robert Israel, Table of n, a(n) for n = 1..1000

Cf. A121878, A167906, A256271.

Res:= 1: count:= 1: v:= 1:
Cands:= [$2..1000]:
for n from 2 do
  found:= false;
  for j from 1 to nops(Cands) do
    if numtheory:-issqrfree(v + Cands[j]^2) then
      found:= true;
      if n = Cands[j] then Res:= Res, n; count:= count+1 fi;
      v:= Cands[j]^2;
      Cands:= subsop(j=NULL, Cands);
      break
    fi
  od;
  if not found then break fi;
od:
Res; # Robert Israel, Jul 16 2019

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

cp's OEIS Frontend

A167904 A121878(A121878(n)).

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A167905 Inverse integer permutation to A121878.

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A258766 Fixed points in A256271.

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