A381598 Index of first term of three consecutive n's in A381597.
1, 9, 34, 147, 111, 359, 437, 389, 594, 826, 1102, 83317, 1789, 5142, 2931, 12671
Offset: 1
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a(1) = a(2) = a(3) = 1. As 1 has now appeared in three terms satisfying a(n) = a(n+k) = a(n+2*k) = 1, with k = 1 in this instance, no other three terms equalling 1 can appear anywhere in the sequence that would satisfy a similar relationship. a(4) = a(5) = 2 as choosing 1 would create another three terms equalling 1 separated by 1, and three terms equalling 1 separated by 2, namely a(1), a(3), a(5). As neither of those is permitted, the next smallest number 2 is chosen. a(6) = 1 as this does not create any three terms equalling 1 separated by any value k, so 1 is again chosen. a(10) = 2 as choosing 1 would create three terms a(2) = a(6) = a(10) = 1 with a difference of 4 which is not permitted. Note that a(9) = a(10) = a(11) = 2, so no other three terms equalling 2 can appear anywhere in the sequence that would satisfy a(n) = a(n+k) = a(n+2*k) = 2. a(11) = 3 as choosing 1 would create three terms a(3) = a(7) = a(11) = 1 with a difference of 4, while choosing 2 would create a(9) = a(10) = a(11) = 2 with a difference of 1. As neither is permitted the next smallest number 3 is chosen.
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