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A243901
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Positive integers n such that p_{n+i} is a quadratic residue modulo p_{n+j} for any distinct i and j among 0, 1, ..., 6
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1
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178633, 2355662, 4892172, 5702347, 9256159, 9572343, 13837265, 15147032, 15429648, 15822376, 16603935, 20925043, 22128672, 22462201, 22689295, 27145167, 28031877, 28470899, 29246422, 30772941, 31211796, 32372758
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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 p_{n+i} is a quadratic residue modulo p_{n+j} for any distinct i and j among 0, 1, ..., m.
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LINKS
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EXAMPLE
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a(1) = 178633 since any 6 primes among the 7 integers prime(178633) = 2434589, prime(178634) = 2434609, prime(178635) = 2434613, prime(178636) = 2434657, prime(178637) = 2434669, prime(178638) = 2434673 and prime(178639) = 2434681 are quadratic residues modulo the remaining one of the 7 primes.
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MATHEMATICA
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q[i_, j_]:=JacobiSymbol[Prime[i], Prime[j]]
m=0; Do[Do[If[q[n+i, n+j]==-1, Goto[aa]], {i, 0, 6}, {j, 0, 6}]; m=m+1; Print[m, " ", n]; Label[aa]; Continue, {n, 1, 32372758}]
Reap[ Do[ If[ Catch[ Do[ If[ JacobiSymbol[Prime[n + i], Prime[n + j]] != 1, Throw@False], {i, 0, 5}, {j, i + 1, 6}]; True], Sow[n]], {n, 32372758}]][[2, 1]] (* Michael Somos, Jun 15 2014 *)
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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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