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A244266
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Positive integers n such that all those prime(n+i) + prime(n+j) (i,j = 0..7) are squarefree.
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3
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4937487, 7763129, 8572423, 8770977, 14024923, 15515130, 18297902, 18935975, 20755826, 20986868, 22661767, 25060321, 26606907, 28884783, 29283671
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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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}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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