A244266 Positive integers n such that all those prime(n+i) + prime(n+j) (i,j = 0..7) are squarefree.

4937487, 7763129, 8572423, 8770977, 14024923, 15515130, 18297902, 18935975, 20755826, 20986868, 22661767, 25060321, 26606907, 28884783, 29283671

Offset

1,1

Comments

Conjecture: For any integer m > 0, there are infinitely many positive integers n such that all those prime(n+i) + prime(n+j) (i,j = 0, ..., m) are squarefree.

Links

Table of n, a(n) for n=1..15.

Example

 a(1) = 4937487, and the 8 consecutive primes prime(4937487+i) (i = 0..7) have the values 84885631, 84885643, 84885667, 84885679, 84885727, 84885739, 84885751,84885763 respectively. The sum of any two of the 8 consecutive primes is squarefree.

Mathematica

SFQ[n_]:=SquareFreeQ[n]
m=0; LL[n_]:=Sum[Boole[Mod[Prime[n+i], 4]==1], {i, 0, 7}]
Do[If[LL[n]>0&&LL[n]<8, Goto[aa]]; Do[If[SFQ[Prime[n+i]+Prime[n+j]]==False, Goto[aa]], {j, 1, 7}, {i, 0, j-1}]; m=m+1; Print[m, " ", n]; Label[aa]; Continue, {n, 1, 29283671}]

Crossrefs

Cf. A000040, A005117, A244254, A244264.

Sequence in context: A089234 A178136 A143687 * A222976 A157804 A151646

Adjacent sequences: A244263 A244264 A244265 * A244267 A244268 A244269

Keyword

nonn

Author

Zhi-Wei Sun, Jun 24 2014

Status

approved