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a(n) is the start of the least run of exactly n consecutive positive integers with strictly increasing values of A071626, or -1 if no such run exists.
1

%I #6 Sep 26 2022 20:16:08

%S 7,1,736,26048,991434

%N a(n) is the start of the least run of exactly n consecutive positive integers with strictly increasing values of A071626, or -1 if no such run exists.

%C a(n) is the least number k such that A071626(k) < A071626(k+1) < ... < A071626(k+n-1), but A071626(k-1) >= A071626(k) if k>1 and A071626(k+n-1) >= A071626(k+n).

%C a(6) > 10^7, if it exists.

%e a(1) = 7 since 7 is the least positive integer that does not belong to a run of increasing values of A071626 with a length of at least 2.

%e a(3) = 736 since A071626(735) = A071626(736) = 26 < A071626(737) = 27 < A071626(738) = A071626(739) = 28, and 736 is the least number with this property.

%Y Cf. A071626, A342091, A357388, A357391.

%K nonn,hard,more

%O 1,1

%A _Amiram Eldar_, Sep 26 2022