A258766 Fixed points in A256271.

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

1,2

Comments

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)

Links

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

Maple

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

Prog

(PARI) 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++)

Crossrefs

Cf. A121878, A167906, A256271.

Sequence in context: A041659 A042043 A178196 * A056722 A181225 A143876

Adjacent sequences: A258763 A258764 A258765 * A258767 A258768 A258769

Keyword

nonn,look

Author

Derek Orr, Jun 09 2015

Status

approved