A256271 a(1) = 1; for n > 1, a(n) is the smallest number not already in the sequence such that a(n)^2 + a(n-1)^2 is squarefree.

1, 2, 3, 5, 4, 7, 6, 11, 8, 9, 10, 13, 12, 17, 14, 15, 16, 19, 18, 23, 20, 27, 22, 25, 21, 26, 29, 24, 31, 28, 33, 32, 35, 34, 39, 38, 37, 30, 41, 36, 43, 40, 47, 42, 53, 44, 45, 46, 49, 48, 59, 50, 51, 52, 55, 54, 61, 56, 57, 58, 63, 62, 65, 64, 67, 60, 71, 66, 73, 68, 69, 70, 79, 74, 75, 76, 77, 72, 83, 78, 85

Offset

1,2

Comments

This is conjectured to be a permutation of the natural numbers.

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000

Mathematica

a={1}; While[Length[a]<1000, e=Last@a; s = Select[ Complement[ Range@e, a], SquareFreeQ[e^2 + #^2]&, 1]; If[s!={}, s=s[[1]], s=e+1; While[ MemberQ[a, s] || !SquareFreeQ[ e^2 + s^2], s++]]; AppendTo[a, s]]; a (* first 1000 terms, Giovanni Resta, Jun 02 2015 *)

Prog

(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

Crossrefs

Cf. A121878, A256270.

Sequence in context: A335535 A276346 A123882 * A293977 A282649 A102454

Adjacent sequences: A256268 A256269 A256270 * A256272 A256273 A256274

Keyword

nonn,easy

Author

Derek Orr, Jun 01 2015

Status

approved