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

1,1

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

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 *)

Crossrefs

Cf. A005117, A077224, A214735.

Sequence in context: A085902 A051083 A051097 * A235618 A076201 A129668

Adjacent sequences: A214770 A214771 A214772 * A214774 A214775 A214776

Keyword

nonn

Author

Zak Seidov, Jul 28 2012

Status

approved