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

Author

Zak Seidov, Jul 28 2012

Keywords

• nonn

Comments

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

Links

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

Crossrefs

Cf. A203988, A214735.

Programs

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

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