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%I #6 Aug 09 2021 21:10:38
%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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