A214735 -id:A214735 - cp's OEIS frontend

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

Zak Seidov, Jul 28 2012

nonn

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.

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

Cf. A005117, A077224, A214735.

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 *)

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.

Original entry on oeis.org

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

Zak Seidov, Jul 28 2012

nonn

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

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

Cf. A203988, A214735.

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

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

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A214773 Primes such that all pairwise sums are squarefree.

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