A214773 Primes such that all pairwise sums are squarefree.

2, 3, 11, 19, 59, 83, 127, 163, 199, 227, 271, 311, 383, 419, 443, 811, 911, 919, 1063, 1163, 1171, 1319, 1427, 1559, 2099, 2143, 2543, 2683, 2999, 3259, 4519, 5099, 5171, 5711, 5783, 6211, 6719, 8111, 8219, 9203, 11003, 12227, 12511, 12659, 13259, 13883

Offset: 1

Author

Zak Seidov, Jul 28 2012

Keywords

• nonn

Comments

a(n+1) is the smallest prime p > a(n) such that all sums a(i)+p, i-1..n are squarefree. All odd terms = 3 mod 4.

The sequence is apparently infinite.

Links

• Zak Seidov, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A005117, A077224, A214735.

Programs

Mathematica

sumsSqFree[t_, p_] := And @@ SquareFreeQ /@ (t + p); t = {2}; Do[p = NextPrime[t[[-1]]]; While[! sumsSqFree[t, p], p = NextPrime[p]]; AppendTo[t, p], {50}]; t (* T. D. Noe, Jul 30 2012 *)