A214802 a(n+1) is the smallest integer m > a(n) such that all of sums (a(i))^2 + m^2, i=1..n are squarefree.

1, 2, 3, 5, 13, 17, 23, 37, 49, 53, 67, 83, 97, 101, 103, 113, 137, 149, 151, 163, 167, 173, 263, 317, 337, 347, 353, 383, 401, 433, 451, 487, 503, 551, 563, 601, 701, 751, 773, 947, 967, 977, 983, 1013, 1033, 1049, 1051, 1087, 1187, 1201, 1249, 1283, 1333

Offset

1,2

Comments

All terms except for a(2)=2 are odd.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..1000

Mathematica

s={1}; m=1; Do[f=0; Do[If[!SquareFreeQ[s[[i]]^2+p^2], f=1; Break[]], {i, m}]; If[f<1, AppendTo[s, p]; m++], {p, 2, 10^3}]; s

Prog

(PARI) v=List([1]); for(m=2, 1e3, for(j=1, #v, if(issquare(m^2+v[j]^2), next(2))); listput(v, m)); Vec(v) \\ Charles R Greathouse IV, Jul 30 2012

Crossrefs

Cf. A203988, A214735.

Sequence in context: A038983 A235635 A253645 * A262840 A215318 A186945

Adjacent sequences: A214799 A214800 A214801 * A214803 A214804 A214805

Keyword

nonn

Author

Zak Seidov, Jul 28 2012

Status

approved