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A066828 Numbers k that divide the average of prime(k-1) and prime(k+1). 0

%I

%S 4,5,11,12,70,72,1053,6459,6460,40083,251742,637320,637322,637330,

%T 10553828,69709721,179992913,179992922,465769813,1208198617,

%U 1208198629,3140421742,3140421769,3140421866,8179002192,8179002205,8179002209

%N Numbers k that divide the average of prime(k-1) and prime(k+1).

%C Each cluster of candidates is about e (2.71828...) times as large as the previous one.

%e The average of prime(4) = 7 and prime(6) = 13 is 10, which is divisible by 5, so 5 is a term of the sequence.

%t a = 0; b = 1; c = 2; Do[ c = Prime[ n + 1 ]; If[ IntegerQ[ (a + c)/(2n) ], Print[ n ] ]; a = b; b = c, {n, 1, 2 10^9} ]

%Y Cf. A066706.

%K nonn

%O 1,1

%A _Robert G. Wilson v_, Jan 20 2002

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Last modified September 21 04:10 EDT 2021. Contains 347596 sequences. (Running on oeis4.)