A289171 Irregular triangle T(n, k) read by rows with 1 <= k <= n: T(n, 1) = A020900(n - k + 1) - (n - k + 1) and T(n, k) = max(0, T(n - 1, k - 1) - 1) otherwise.
1, 1, 1, 2, 3, 1, 3, 2, 4, 2, 1, 4, 3, 1, 5, 3, 2, 6, 4, 2, 1, 7, 5, 3, 1, 9, 6, 4, 2, 9, 8, 5, 3, 1, 9, 8, 7, 4, 2, 9, 8, 7, 6, 3, 1, 11, 8, 7, 6, 5, 2, 13, 10, 7, 6, 5, 4, 1, 12, 12, 9, 6, 5, 4, 3, 13, 11, 11, 8, 5, 4, 3, 2, 14, 12, 10, 10, 7, 4, 3, 2, 1
Offset: 1
Examples
Triangle begins: n a(n) 1: 0 2: 1 3: 1 4: 2 5: 3 1 6: 3 2 7: 4 2 1 8: 4 3 1 9: 5 3 2 10: 6 4 2 1 11: 7 5 3 1 12: 9 6 4 2 13: 9 8 5 3 1 14: 9 8 7 4 2 15: 9 8 7 6 3 1 16: 11 8 7 6 5 2 17: 13 10 7 6 5 4 1 18: 12 12 9 6 5 4 3 19: 13 11 11 8 5 4 3 2 20: 14 12 10 10 7 4 3 2 1 ...
Links
- Michael De Vlieger, Table of n, a(n) for n = 1..13692 (rows 1 <= n <= 250).
Programs
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Mathematica
T[n_, k_] := T[n, k] = If[k == 1, PrimePi[2 Prime@ #] - # &[n - k + 1], Max[0, T[n - 1, k - 1] - 1]]; Map[DeleteCases[#, 0] &, Table[T[n, k], {n, 20}, {k, n}]] // Flatten (* or *) T[n_, k_] := T[n, k] = If[k == 1, PrimePi[2 Prime@ #] - # &[n - k + 1], Max[0, T[n - 1, k - 1] - 1]]; Table[T[n, k], {n, 60}, {k, Count[Range[# + 1, 2 # - 1] &@ Prime[n + 1], s_ /; PrimeOmega@ s == 2 && EvenQ@ s]}] // Flatten (* Michael De Vlieger, Jul 21 2017 *)
Formula
Row lengths = A107347(n + 1).
Comments